{"id":11351,"date":"2022-03-06T14:14:20","date_gmt":"2022-03-06T08:44:20","guid":{"rendered":"https:\/\/envisionmathanswerkey.com\/?p=11351"},"modified":"2022-03-15T09:40:57","modified_gmt":"2022-03-15T04:10:57","slug":"envision-math-common-core-grade-5-answer-key-topic-6","status":"publish","type":"post","link":"https:\/\/envisionmathanswerkey.com\/envision-math-common-core-grade-5-answer-key-topic-6\/","title":{"rendered":"enVision Math Common Core Grade 5 Answer Key Topic 6 Use Model Strategies to Divide Decimals"},"content":{"rendered":"

Go through the\u00a0enVision Math Common Core Grade 5 Answer Key<\/a>\u00a0Topic 6 Use Models and Strategies to Divide Decimals<\/strong>\u00a0regularly and improve your accuracy in solving questions.<\/p>\n

enVision Math Common Core 5th Grade Answers Key Topic 6 Use Model Strategies to Divide Decimals<\/h2>\n

\"Envision
\nenVision STEM Project: States of Water
\nDo Research<\/strong>
\nUse the Internet or other sources to learn about the states of water. Find at least 5 examples of water in nature as a solid, as a liquid, and as a gas. At what temperature does liquid water change to ice? At what temperature does liquid water change to water vapor?<\/p>\n

Journal: Write a Report<\/strong> Include what you found. Also in your report:
\n\u2022 Explain how liquid water changes to ice and to water vapor.
\n\u2022 At 23\u00b0F, 1 inch of rain equals 10 inches of snow. Convert 2 inches of rainfall to snowfall.
\n\u2022 Make up and solve division problems that involve decimals.<\/p>\n

Review What You Know<\/strong><\/p>\n

Vocabulary<\/strong><\/p>\n

Choose the best term from the box. Write it on the blank.
\n\u2022 decimal
\n\u2022 dividend
\n\u2022 divisor
\n\u2022 quotient<\/p>\n

Question 1.
\n_____ is the name for the answer to a division problem.
\nAnswer:
\nQuotient<\/strong> is the name for the answer to a division problem.<\/p>\n

Question 2.
\nA number that is being divided by another number is called the _____
\nAnswer:
\nA number that is being divided by another number is called the dividend<\/strong>.<\/p>\n

Whole Number Operations<\/strong><\/p>\n

Find each value.<\/p>\n

Question 3.
\n9,007 \u2013 3,128
\nAnswer:
\n9,007 – 3,128 = 5,879
\nExplanation:
\nThe properties of whole numbers are based on arithmetic operations such as addition, subtraction, division and multiplication. Subtraction of two whole numbers may not result in whole numbers. It can be an integer too. Whole numbers are positive integers along with zero. They are all the natural numbers including zero. Subtract 3,128 from 9,007 then the difference is 5,879.
\nQuestion 4.
\n725,864 + 39,798
\nAnswer:
\n725,864 + 39,798 = 765,662
\nExplanation:
\nThe properties of whole numbers are based on arithmetic operations such as addition, subtraction, division and multiplication. Two whole numbers if added or multiplied will give a whole number itself. Whole numbers are positive integers along with zero. They are all the natural numbers including zero. Perform addition operation on these two numbers 725,864 and 39,798 then the sum is 765,662.<\/p>\n

Question 5.
\n35 \u00d7 17
\nAnswer:
\n35 \u00d7 17 = 595
\nExplanation:
\nThe properties of whole numbers are based on arithmetic operations such as addition, subtraction, division and multiplication. Two whole numbers if added or multiplied will give a whole number itself. Whole numbers are positive integers along with zero. They are all the natural numbers including zero. Perform multiplication operation on these two numbers 35 and 17 then the result is 595.<\/p>\n

Question 6.
\n181 \u00d7 42
\nAnswer:
\n181 \u00d7 42 = 7,602
\nExplanation:
\nThe properties of whole numbers are based on arithmetic operations such as addition, subtraction, division and multiplication. Two whole numbers if added or multiplied will give a whole number itself.\u00a0 Whole numbers are positive integers along with zero. They are all the natural numbers including zero. Perform multiplication operation on these two numbers 181 and 42 then the result is 7,602.<\/p>\n

Question 7.
\n768 \u00f7 6
\nAnswer:
\n768 \u00f7 6 = 128
\nExplanation:
\nThe properties of whole numbers are based on arithmetic operations such as addition, subtraction, division and multiplication. The inverse operation of multiplication is division. Whole numbers are positive integers along with zero. They are all the natural numbers including zero. Perform division operation on these two numbers 768 and 6. Here 768 is dividend and 6 is divisor then the quotient is 128.<\/p>\n

Question 8.
\n506 \u00f7 22
\nAnswer:
\n506 \u00f7 22 = 23
\nThe properties of whole numbers are based on arithmetic operations such as addition, subtraction, division and multiplication. The inverse operation of multiplication is division. Whole numbers are positive integers along with zero. They are all the natural numbers including zero. Perform division operation on these two numbers 506 and 22. Here 506 is dividend and 22 is divisor then the quotient is 23.<\/p>\n

Question 9.
\n6,357 \u00f7 60
\nAnswer:
\n6,357 \u00f7 60 = 105.95
\nExplanation:
\nThe properties of whole numbers are based on arithmetic operations such as addition, subtraction, division and multiplication. The inverse operation of multiplication is division. Whole numbers are positive integers along with zero. They are all the natural numbers including zero. Perform division operation on these two numbers 6357 and 60. Here 6,357 is dividend and 60 is divisor then the quotient is 105.95.<\/p>\n

Question 10.
\n3,320 \u00f7 89
\nAnswer:
\n3,320 \u00f7 89 = 37.30
\nExplanation:
\nThe properties of whole numbers are based on arithmetic operations such as addition, subtraction, division and multiplication. The inverse operation of multiplication is division. Whole numbers are positive integers along with zero. They are all the natural numbers including zero. Perform division operation on these two numbers 3,320 and 89. Here 3,320 is dividend and 89 is divisor then the quotient is 37.30.<\/p>\n

Question 11.
\n88,888 \u00f7 20
\nAnswer:
\n88,888 \u00f7 20 = 4,444.4
\nExplanation:
\nThe properties of whole numbers are based on arithmetic operations such as addition, subtraction, division and multiplication. The inverse operation of multiplication is division. Whole numbers are positive integers along with zero. They are all the natural numbers including zero. Perform division operation on these two numbers 88,888 and 20. Here 88,888 is dividend and 20 is divisor then the quotient is 4,444.4.<\/p>\n

Rounding Decimals<\/strong>
\nRound each number to the place of the underlined digit.<\/p>\n

Question 12.
\n0.3<\/u>4
\nAnswer:
\n0.3
\nExplanation:
\nRounding is a\u00a0process to estimate a particular number in a context. To round a number look at the next digit in the right place, if the digit is less than 5, round down and if the digit is 5 or more than 5, round up.\u00a0The number 0.3<\/u>4 is rounded to 0.3.<\/p>\n

Question 13.
\n96<\/u>.5
\nAnswer:
\n97
\nExplanation:
\nRounding is a process to estimate a particular number in a context. To round a number look at the next digit in the right place, if the digit is less than 5, round down and if the digit is 5 or more than 5, round up. The number 96<\/u>.5 is rounded to 97.<\/p>\n

Question 14.
\n81.2<\/u>7
\nAnswer:
\n81.3
\nExplanation:
\nRounding is a process to estimate a particular number in a context. To round a number look at the next digit in the right place, if the digit is less than 5, round down and if the digit is 5 or more than 5, round up. The number 81.2<\/u>7 is rounded to 81.3.<\/p>\n

Question 15.
\n2<\/u>05.3
\nAnswer:
\n205
\nExplanation:
\nRounding is a process to estimate a particular number in a context. To round a number look at the next digit in the right place, if the digit is less than 5, round down and if the digit is 5 or more than 5, round up. The number 2<\/u>05.3 is rounded to 205.<\/p>\n

Decimals<\/strong><\/p>\n

Question 16.
\nAn insect measured 1.25 cm long. Which number is less than 1.25?
\nA. 1.35
\nB. 1.3
\nC. 1.26
\nD. 1.2
\nAnswer:
\nOption D is correct.
\nExplanation:
\nAn insect measured 1.25 cm long. We have to find out the number less than 1.25.
\nA. 1.35 is greater than 1.25. So option A is not correct.
\nB. 1.3 is greater than 1.25. So option B is not correct.
\nC. 1.26 is greater than 1.25 . So option C is not correct.
\nD. 1.2 is less than 1.25. So option D is correct.<\/p>\n

Question 17.
\nExplain<\/strong> The grid in this model represents 1. What decimal does the shaded part represent? Explain.
\n\"Envision
\nAnswer:
\n0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.04 = 0.64
\nThe shaded part represents the decimal 0.64.
\nExplanation:
\nThe above grid represents 1. In that grid 1 column is shaded. The shaded part decimal value is 0.1. The second column shaded part decimal value is 0.1. The third column shaded part decimal value is 0.1. The fourth column shaded part decimal value is 0.1. The fifth column shaded part decimal value is 0.1. The sixth column shaded part decimal value is 0.1. The seventh column shaded part decimal value is 0.04. By adding these columns decimal values the sum is 0.64.<\/p>\n

Decimal Operations<\/strong><\/p>\n

Find each value.<\/p>\n

Question 18.
\n23.7 \u2013 11.82
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-6(1)\"
\n23.7 – 11.82 = 11.88
\nExplanation:
\nFour basic operations on decimals are addition, subtraction, multiplication and division. To add decimals numbers we follow this step.
\nStep 1: Write numbers under each other and line up vertically the decimal points.
\nPerform subtraction operation on these two numbers 23.7 and 11.82. Subtract 11.82 from 23.7 then the difference is 11.88.<\/p>\n

Question 19.
\n66.8 + 3.64
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-6(2)\"
\n66.8 + 3.64 = 70.44
\nExplanation:
\nFour basic operations on decimals are addition, subtraction, multiplication and division. To add decimals numbers we follow this step.
\nStep 1: Write numbers under each other and line up vertically the decimal points.
\nPerform addition operation on these two numbers 66.8 and 3.64. Add 66.8 with 3.64 then the sum is 70.44.<\/p>\n

Question 20.
\n9 \u00d7 1.4
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-6(3)\"
\n9 x 1. 4 = 12. 6
\nExplanation:
\nFour basic operations on decimals are addition, subtraction, multiplication and division. To add decimals numbers we follow this step.
\nStep 1: Write numbers under each other and line up vertically the decimal points.
\nPerform multiplication operation on these two numbers 9 and 1.4. Multiply 9 with 1.4 then the result is 12.6.<\/p>\n

Question 21.
\n3.2 \u00d7 7.6
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-6(4)\"
\n3.2 x 7.6 = 24.32
\nExplanation:
\nFour basic operations on decimals are addition, subtraction, multiplication and division. To add decimals numbers we follow this step.
\nStep 1: Write numbers under each other and line up vertically the decimal points.
\nPerform multiplication operation on these two numbers 3.2 and 7.6. Multiply 3.2 with 7.6 then the result is 24.32.<\/p>\n

Pick a Project<\/strong><\/p>\n

PROJECT 6A<\/strong>
\nCan you throw a dinner party?
\nProject: Plan a Party
\n\"Envision<\/p>\n

PROJECT 6B<\/strong>
\nHow much does it cost to run a company?
\nProject: Build a Company
\n\"Envision<\/p>\n

PROJECT 6C<\/strong>
\nHow do you organize food?
\nProject: Open Your Own Fruit Stand
\n\"Envision<\/p>\n

PROJECT 6D<\/strong>
\nWould you like to build a house?
\nProject: Draw Plans for a Doll House
\n\"Envision<\/p>\n

Lesson 6.1 Patterns for Dividing with Decimals<\/h3>\n

Activity<\/strong><\/p>\n

Solve & Share<\/strong><\/p>\n

An object is 279.4 centimeters wide. If you divide the object into 10 equal parts, how wide will each part be? Solve this problem any way you choose.<\/p>\n

How can you use structure and the relationship between multiplication and division to help you?
\n\"Envision<\/p>\n

Look Back!<\/strong> What do you notice about the width of the object and the width of each part?
\nAnswer:
\nThe width of the object is 279.4
\n279.4\/10 = 27.94
\nThe width of each part is 27.94
\nExplanation:
\nAn object is 279.4 centimeters wide. If we divide the object into 10 equal parts. The wide of the each part is 27.94.
\nMultiplication and division\u00a0are the reverse or opposite of each other in that when we divide, we break apart, and when we multiply, we put together.<\/p>\n

Visual Learning Bridge<\/strong>
\nEssential Question<\/strong> How Can You Divide Question Decimals by Powers of 10?<\/p>\n

A.<\/strong>
\nShondra wants to cut a cloth into 10 strips. All the strips should be exactly the same size. You can use place value and what you know about whole numbers to divide decimals by powers of 10. How long will each strip be?<\/p>\n

You can divide to find equal parts of a whole.
\n\"Envision<\/p>\n

\"Envision<\/p>\n

Remember that
\n10 = 10!
\n\"Envision<\/p>\n

B.<\/strong>
\nFind 89.5 \u00f7 10.
\nPlace value is based on 10. The value of each place is \\(\\frac{1}{10}\\) the value of the place to the left. Dividing by 10 results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left.
\n\"Envision
\n89.5 \u00f7 101<\/sup> = 8.95
\nEach cloth strip will be 8.95 cm long.<\/p>\n

Convince Me!<\/strong> Use Structure Celinda thought of 89.5 in parts, 80 + 9 + 0.5, and divided each part: 80 \u00f7 10 = 8; 9 \u00f7 10 = \\(\\frac{9}{10}\\) or 0.9; 0.5 \u00f7 10 = 0.05. Then she added the parts to get 8.95. What do you notice?
\nAnswer:
\nCelinda divided 89.5 into parts as 80 + 9 + 0.5, and divided each part 80 \u00f7 10 = 8; 9 \u00f7 10 = 0.9; 0.5 \u00f7 10 = 0.05. Then she added the parts to get 8.95. I notice when we divide the number 89.5 with 10 then the result is 8.95 and dividing 89.5 into parts also we get same result as 8.95.<\/p>\n

Guided Practice999<\/strong><\/p>\n

Do You Understand?<\/strong><\/p>\n

Question 1.
\nSuppose Shondra wanted to cut the cloth into 102<\/sup> strips. How long would each strip be?
\nAnswer:
\n89.5 \u00f7 102<\/sup>
\n89.5 \u00f7 100 = 0.895
\nEach cloth strip will be 0.895 cm long.
\nExplanation:
\nShondra wanted to cut the cloth into 102<\/sup> strips. Place value is based on 102<\/sup>. The value of each place is 1\/100 the value of the place to the left. Dividing by 102<\/sup> results in moving each digit two places to the right. This looks the same as moving the decimal point two places to the left. Each cloth strip will be 0.895 cm long.<\/p>\n

Question 2.
\nKrista divides a number by 10. Then she divides the same number by 50. Which quotient is greater? How can you tell?
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-6.12(1)\"
\nThe quotient 10 is greater.
\nExplanation:
\nIn the above image we can observe the quotient 10 and 2. Krista divides the number 100 by 10 then the quotient is 10. Then she divides the same number 100 by 50 then the quotient is 2. The quotient 10 is greater.<\/p>\n

Do You Know How?<\/strong><\/p>\n

In 3-10, use mental math to find each quotient.<\/p>\n

Question 3.
\n370.2 \u00f7 102<\/sup>
\nAnswer:
\n370.2 \u00f7 102<\/sup>
\n370.2 \u00f7 100 = 3.702
\nExplanation:
\nIn the above division method the place value is based on 102<\/sup>. The value of each place is 1\/100 the value of the place to the left. Dividing the number 370.2 by 102<\/sup> results in moving each digit two places to the right. This looks the same as moving the decimal point two places to the left. The quotient for 370.2 \u00f7 100 = 3.702.<\/p>\n

Question 4.
\n126.4 \u00f7 101<\/sup>
\nAnswer:
\n126.4 \u00f7 101<\/sup>
\n126.4 \u00f7 10 = 12.64
\nExplanation:
\nIn the above division method the place value is based on 101<\/sup>. The value of each place is 1\/10 the value of the place to the left. Dividing the number 126.4 by 101<\/sup> results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 126.4 \u00f7 10 = 12.64.<\/p>\n

Question 5.
\n7.25 \u00f7 10
\nAnswer:
\n7.25 \u00f7 10 = 0.725
\nExplanation:
\nIn the above division method the place value is based on 10. The value of each place is 1\/10 the value of the place to the left. Dividing the number 7.25 by 10 results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 7.25 \u00f7 10 = 0.725.<\/p>\n

Question 6.
\n72.5 \u00f7 103<\/sup>
\nAnswer:
\n72.5 \u00f7 103<\/sup>
\n72.5 \u00f7 1000 = 0.0725
\nExplanation:
\nIn the above division method the place value is based on 103<\/sup>. The value of each place is 1\/1000 the value of the place to the left. Dividing the number 72.5 by 103<\/sup> results in moving each digit three places to the right. This looks the same as moving the decimal point three places to the left. The quotient for 72.5 \u00f7 1000 = 0.0725.<\/p>\n

Question 7.
\n281.4 \u00f7 100<\/sup>
\nAnswer:
\n281.4 \u00f7 100<\/sup>
\n281.4 \u00f7 1 = 281.4
\nExplanation:
\nIn the above division method the place value is based on 100<\/sup>. The value of each place is 1 the value of the place to the left. Dividing the number 281.4 by 1 results in moving each digit zero places to the right. This looks the same as moving the decimal point zero places to the left. The quotient for 281.4 \u00f7 1 = 281.4.<\/p>\n

Question 8.
\n2,810 \u00f7 104
\n<\/sup>Answer:
\n2,810 \u00f7 104<\/sup>
\n2,810 \u00f7 10000 = 0.2810
\nExplanation:
\nIn the above division method the place value is based on 104<\/sup>. The value of each place is 1\/10000 the value of the place to the left. Dividing the number 2,810 by 104<\/sup> results in moving each digit four places to the right. This looks the same as moving the decimal point four places to the left. The quotient for 2,810 \u00f7 10000 = 0.2810.<\/p>\n

Question 9.
\n3,642.4 \u00f7 102<\/sup>
\nAnswer:
\n3,642.4 \u00f7 102<\/sup>
\n3,642.4 \u00f7 100 = 36.424
\nExplanation:
\nIn the above division method the place value is based on 102<\/sup>. The value of each place is 1\/100 the value of the place to the left. Dividing the number 3,642.4 by 102<\/sup> results in moving each digit two places to the right. This looks the same as moving the decimal point two places to the left. The quotient for 3,642.4 \u00f7 100 = 36.424.<\/p>\n

Question 10.
\n364.24 \u00f7 101<\/sup>
\nAnswer:
\n364.24 \u00f7 101<\/sup>
\n364.24 \u00f7 10 = 36.424
\nExplanation:
\nIn the above division method the place value is based on 101<\/sup>. The value of each place is 1\/10 the value of the place to the left. Dividing the number 364.24 by 101<\/sup> results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 364.24 \u00f7 10 = 36.424.<\/p>\n

Independent Practice<\/strong><\/p>\n

Leveled Practice<\/strong> in 11-25, find each quotient. Use mental math.<\/p>\n

Question 11.
\n4,600 \u00f7 10
\n460 \u00f7 10
\n46 \u00f7 10
\n4.6 \u00f7 10
\nAnswer:
\n4,600 \u00f7 10 = 460
\n460 \u00f7 10 = 46
\n46 \u00f7 10 = 4.6
\n4.6 \u00f7 10 = 0.46
\nExplanation:
\nIn the above division method the place value is based on 10. The value of each place is 1\/10 the value of the place to the left.
\nDividing the number 4,600 by 10 results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 4,600 \u00f7 10 = 460.
\nDividing the number 460 by 10 results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 460 \u00f7 10 = 46.
\nDividing the number 46 by 10 results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 46 \u00f7 10 = 4.6.
\nDividing the number 4.6 by 10 results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 4.6 \u00f7 10 = 0.46.<\/p>\n

Question 12.
\n134.4 \u00f7 103<\/sup>
\n134.4 \u00f7 102<\/sup>
\n134.4 \u00f7 101<\/sup>
\n134.4 \u00f7 100<\/sup>
\nAnswer:
\n134.4 \u00f7 103\u00a0<\/sup>
\n134.4 \u00f7 1000 = 0.1344<\/strong>
\n134.4 \u00f7 102<\/sup>
\n134.4 \u00f7 100 = 1.344<\/strong>
\n134.4 \u00f7 101<\/sup>
\n134.4 \u00f7 10 = 13.44<\/strong>
\n134.4 \u00f7 100<\/sup>
\n134.4 \u00f7 1 = 134.4\u00a0<\/strong><\/p>\n

Explanation:
\nDividing the number 134.4 by 103<\/sup> results in moving each digit three places to the right. This looks the same as moving the decimal point three places to the left. The quotient for 134.4 \u00f7 1000 = 0.1344.
\nDividing the number 134.4 by 102<\/sup> results in moving each digit two places to the right. This looks the same as moving the decimal point two places to the left. The quotient for 134.4 \u00f7 100 = 1.344.
\nDividing the number 134.4 by 101<\/sup> results in moving each digit one two place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 134.4 \u00f7 10 = 13.44.
\nDividing the number 134.4 by 100<\/sup> results in moving each digit zero places to the right. This looks the same as moving the decimal point zero places to the left. The quotient for 134.4 \u00f7 1 = 134.4.
\nQuestion 13.
\n98.6 \u00f7 1
\n98.6 \u00f7 100
\n98.6 \u00f7 10
\n98.6 \u00f7 1,000
\nAnswer:
\n98.6 \u00f7 1
\n98.6 \u00f7 1 = 98.6<\/strong>
\n98.6 \u00f7 100
\n98.6 \u00f7 100 = 0.986<\/strong>
\n98.6 \u00f7 10
\n98.6 \u00f7 10 = 9.86<\/strong>
\n98.6 \u00f7 1,000
\n98.6 \u00f7 1,000 = 0.0986<\/strong>
\nExplanation:
\nDividing the number 98.6 by 1 results the quotient for 98.6 \u00f7 1 = 98.6.
\nDividing the number 98.6 by 100 results in moving each digit two places to the right. This looks the same as moving the decimal point two places to the left. The quotient for 98.6 \u00f7 100 = 0.986.
\nDividing the number 98.6 by 10 results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 98.6 \u00f7 10 = 9.86.
\nDividing the number 98.6 by 1000 results in moving each digit three places to the right. This looks the same as moving the decimal point three places to the left. The quotient for 98.6 \u00f7 1,000 = 0.0986.<\/p>\n

Question 14.
\n136.5 \u00f7 10
\nAnswer:
\n136.5 \u00f7 10 = 13.65<\/strong>
\nExplanation:
\nIn the above division method the place value is based on 10. The value of each place is 1\/10 the value of the place to the left. Dividing the number 136.5 by 10 results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 136.5 \u00f7 10 = 13.65.<\/p>\n

Question 15.
\n753 \u00f7 100
\nAnswer:
\n753 \u00f7 100 = 7.53<\/strong>
\nExplanation:
\nIn the above division method the place value is based on 100. The value of each place is 1\/100 the value of the place to the left. Dividing the number 753 by 100 results in moving each digit two place to the right. This looks the same as moving the decimal point two places to the left. The quotient for 753 \u00f7 100 = 7.53.<\/p>\n

Question 16.
\n890.1 \u00f7 100<\/sup>
\nAnswer:
\n890.1 \u00f7 1 = 890.1<\/strong>
\nExplanation:
\nIn the above division method the place value is based on 100<\/sup>. Dividing the number 890.1 by 1 results in moving each digit zero places to the right. This looks the same as moving the decimal point zero places to the left. The quotient for 890.1 \u00f7 1 = 890.1.<\/p>\n

Question 17.
\n3.71 \u00f7 102<\/sup>
\nAnswer:
\n3.71 \u00f7 100 = 0.0371<\/strong>
\nExplanation:
\nIn the above division method the place value is based on 102<\/sup>. The value of each place is 1\/100 the value of the place to the left. Dividing the number 3.71 by 102<\/sup>results in moving each digit two places to the right. This looks the same as moving the decimal point two places to the left. The quotient for 3.71 \u00f7 100 = 0.0371<\/strong>.<\/p>\n

Question 18.
\n8,100 \u00f7 104<\/sup>
\nAnswer:
\n8,100 \u00f7 10000 = 0.81<\/strong>
\nExplanation:
\nIn the above division method the place value is based on 104<\/sup>. The value of each place is 1\/10000 the value of the place to the left. Dividing the number 8100 by 104 <\/sup>results in moving each digit four places to the right. This looks the same as moving the decimal point four places to the left. The quotient for 8,100 \u00f7 10000 = 0.81.<\/strong><\/p>\n

Question 19.
\n864 \u00f7 103<\/sup>
\nAnswer:
\n864 \u00f7 1000 = 0.864<\/strong>
\nExplanation:
\nIn the above division method the place value is based on 103<\/sup>. The value of each place is 1\/1000 the value of the place to the left. Dividing the number 864 by 103 <\/sup>results in moving each digit three places to the right. This looks the same as moving the decimal point three places to the left. The quotient for 864 \u00f7 1000 = 0.864.<\/strong><\/p>\n

Question 20.
\n0.52 \u00f7 101<\/sup>
\nAnswer:
\n0.52 \u00f7 10 = 0.052<\/strong>
\nExplanation:
\nIn the above division method the place value is based on 101<\/sup>. The value of each place is 1\/10 the value of the place to the left. Dividing the number 0.52 by 101 <\/sup>results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 0.52 \u00f7 10 = 0.052<\/strong>.<\/strong><\/p>\n

Question 21.
\n15.7 \u00f7 1,000
\nAnswer:
\n15.7 \u00f7 1,000 = 0.157<\/strong>
\nExplanation:
\nIn the above division method the place value is based on 1000. Dividing the number 15.7 by 1000\u00a0<\/sup>results in moving each digit three places to the right. This looks the same as moving the decimal point three places to the left. The quotient for 15.7 \u00f7 1,000 = 0.157<\/strong>.<\/strong><\/p>\n

Question 22.
\n7,700 \u00f7 102<\/sup>
\nAnswer:
\n7,700 \u00f7 100 = 77<\/strong>
\nExplanation:
\nIn the above division method the place value is based on 100. Dividing the number 7,700 by 100\u00a0<\/sup>results in moving each digit two places to the right. This looks the same as moving the decimal point two places to the left. The quotient for 7,700 \u00f7 100 = 77<\/strong>.<\/strong><\/p>\n

Question 23.
\n770 \u00f7 102<\/sup>
\nAnswer:
\n770 \u00f7 100 = 7.7<\/strong>
\nExplanation:
\nIn the above division method the place value is based on 102<\/sup>. The value of each place is 1\/100 the value of the place to the left. Dividing the number 770 by 100\u00a0<\/sup>results in moving each digit two places to the right. This looks the same as moving the decimal point two places to the left. The quotient for 770 \u00f7 100 = 7.7.<\/strong><\/p>\n

Question 24.
\n77 \u00f7 101<\/sup>
\nAnswer:
\n77 \u00f7 10 = 7.7<\/strong>
\nExplanation:
\nIn the above division method the place value is based on 101<\/sup>. The value of each place is 1\/10 the value of the place to the left. Dividing the number 77 by 10\u00a0<\/sup>results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 77 \u00f7 10 = 7.7.<\/strong><\/p>\n

Question 25.
\n7.7 \u00f7 101<\/sup>
\nAnswer:
\n7.7 \u00f7 10 = 0.77<\/strong>
\nExplanation:
\nIn the above division method the place value is based on 101<\/sup>. The value of each place is 1\/10 the value of the place to the left. Dividing the number 7.7 by 10\u00a0<\/sup>results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 7.7 \u00f7 10 = 0.77.<\/strong><\/p>\n

Problem Solving<\/strong><\/p>\n

For 26-28, use the table that shows the winning times at the Pacific Middle School swim meet.<\/p>\n

\"Envision<\/p>\n

Question 26.
\nWhat was the difference between the winning butterfly time and the winning backstroke time?
\nAnswer:
\nThe difference between the winning butterfly time and the winning backstroke time is 4.66 seconds<\/strong>.
\nExplanation:
\nThe winning butterfly time is 58.49 seconds. The winning backstroke time is 53.83 seconds.\u00a0Subtract the winning backstroke time from winning butterfly time then the difference is 4.66 seconds.<\/p>\n

Question 27.
\nThe winning time for the 100-yard freestyle was twice the time for the 50-yard freestyle. What was the winning time for the 100-yard freestyle?
\nAnswer:
\nThe winning time for the 100-yard freestyle is 44.34 seconds<\/strong>.
\nExplanation:
\nThe winning time for the 100-yard freestyle was twice the time for the 50-yard freestyle. The winning time for 50-yard freestyle is 22.17 seconds. So add 22.17 seconds with 22.17 seconds then the sum is 44.34 seconds. The winning time for the 100-yard freestyle is 44. 34 seconds.<\/p>\n

Question 28.
\nWhat was the difference between the winning 100-yard freestyle time and the winning butterfly time?
\nAnswer:
\nThe difference between the winning 100-yard freestyle time and the winning butterfly time is 14.15 seconds<\/strong>.
\nExplanation:
\nThe winning 100-yard freestyle time is 44.34 seconds. The winning 100-yard butterfly time is 58.49 seconds. Subtract 100-yard freestyle winning time from 100-yard butterfly winning time then the difference is 14.15 seconds.<\/p>\n

Question 29.
\nReasoning<\/strong> A pickup truck carrying 103<\/sup> identical bricks weighs 6,755 pounds. If the empty truck weighs 6,240 pounds, what is the weight of each brick? Explain how to solve the problem.
\nAnswer:<\/p>\n

Question 30.
\nHigher Order Thinking<\/strong> Katie noticed a pattern in the answers for each of the expressions below. What do you notice?
\n\"Envision
\nAnswer:
\n14.6 x\u00a0 0.1 = 1.46\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 14.6 \u00f7 10 = 1.46
\n146 x 0.01 = 1.46\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 146 \u00f7 100 = 1.46
\n146 x 0.001 = 0.146\u00a0 \u00a0 \u00a0 \u00a0146 \u00f7 1,000 = 0.146
\nExplanation:
\nIn first expressions I noticed that if we are multiplying 14.6 x\u00a0 0.1 results the product as 1.46. When we are dividing 14.6 \u00f7 10 results the quotient as 1.46.
\nIn second expressions I noticed that if we are multiplying 146 x\u00a0 0.01 results the product as 1.46. When we are dividing 146 \u00f7 100 results the quotient as 1.46.
\nIn third expressions I noticed that if we are multiplying 146 x\u00a0 0.001 results the product as 0.146. When we are dividing 146 \u00f7 1,000 results the quotient as 0.146.<\/p>\n

Assessment Practice<\/strong><\/p>\n

Question 31.
\nChoose the equations in which n = 1,000 makes the equation true.
\n\"Envision 0 2.5 \u00f7 n = 0.025
\n\"Envision 947.5 \u00f7 n = 0.9475
\n\"Envision 8,350 \u00f7 n = 8.35
\n\"Envision 16.4 \u00f7 n = 0.0164
\n\"Envision 0.57 \u00f7 n = 0.0057
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-21\"
\nExplanation:
\nIf we put n = 1,000 in first equation 0.25 \u00f7 1,000 = 0.0025. The First equation is not true.
\nIf we put n = 1,000 in second equation 947.5 \u00f7 1,000 = 0.9475. The Second equation is true.
\nIf we put n = 1,000 in third equation 8,350 \u00f7 1,000 = 8.35. The third equation is true.
\nIf we put n = 1,000 in fourth equation 16.4 \u00f7 1,000 = 0.0164. The fourth equation is true.
\nIf we put n = 1,000 in fifth equation 0.57 \u00f7 1,000 = 0.00057. The fifth equation is not true.<\/p>\n

Question 32.
\nChoose the equations in which d = 102<\/sup> makes the equation true.
\n\"Envision 386.2 \u00f7 d = 3.862
\n\"Envision 4,963.6 \u00f7 d = 4.9636
\n\"Envision 0.6 \u00f7 d = 0.006
\n\"Envision 5.8 \u00f7 d = 0.58
\n\"Envision 15.3 \u00f7 d = 0.153
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-21
\nExplanation:
\nIf we put d = 100 in first equation 386.2 \u00f7 100 = 3.862. The First equation is true.
\nIf we put d = 100 in second equation 4,963.6 \u00f7 100 = 49.636. The Second equation is not true.
\nIf we put d = 100 in third equation 0.6 \u00f7 100 = 0.006. The third equation is true.
\nIf we put d = 100 in fourth equation 5.8 \u00f7 100 = 0.058. The fourth equation is not true.
\nIf we put d = 100 in fifth equation 15.3 \u00f7 100 = 0.153. The fifth equation is true.<\/p>\n

Lesson 6.2 Estimate Decimal Quotients<\/h3>\n

Activity<\/strong><\/p>\n

Slove&Share<\/strong><\/p>\n

A 135.8-foot piece of construction material needs to be cut into pieces that are each 16 feet long. About how many pieces can be cut? Solve this problem any way you choose.<\/p>\n

\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-21.1\"
\n135 \u00f7 15 = 9
\nThe construction material can be cut into 9 pieces.
\nExplanation:
\nA 135.8-foot piece of construction material is about 135. We need to cut the material into pieces that are each 16 feet long. The 16 pieces material is rounded to 15. Apply division method to solve the problem. Divide 135 with 15 then the result is 9. The construction material can be cut into 9 pieces.<\/p>\n

You can use reasoning to estimate decimal quotients.
\n\"Envision<\/p>\n

Look Back! Reasoning<\/strong> Can you find a different way to estimate the answer for the problem above? Explain.<\/p>\n

Visual Learning Bridge<\/strong><\/p>\n

Essential Question<\/strong>
\nHow Can You Use Estimation to Find Quotients?<\/p>\n

A.<\/strong>
\nDiego borrowed money from his parents to purchase a video gaming system for $473.89 (including tax). About how much are his monthly payments to his parents if he wants to pay this off in one year?
\n\"Envision<\/p>\n

You can use division to find equal groups.
\n\"Envision<\/p>\n

B.<\/strong>
\nOne Way<\/strong>
\nEstimate $473.89 \u00f7 12. Use rounding.
\nRound to the nearest ten: 473.89 rounds to 470; 12 rounds to 10
\n$473.89 \u00f7 12 is about $470 \u00f7 10 = $47.
\nEach monthly payment will be about $47.<\/p>\n

C.<\/strong>
\nAnother Way<\/strong>
\nEstimate $473.89 \u00f7 12. Use compatible numbers.
\nLook for compatible numbers.
\n$473.89 \u00f7 12 is close to $480 \u00f7 12 = $40.<\/p>\n

You know 48 \u00f7 12 = 4.
\n\"Envision
\nEach monthly payment will be about $40.<\/p>\n

Convince Me! Construct Arguments<\/strong> in the example above, which estimate is closer to the exact answer? Tell how you decided.
\nAnswer:
\nWe use compatible numbers to make the problem easier to solve in our head by rounding each number to the nearest ten, twenty, fifty or hundred. But if we make the numbers compatible and round up to the nearest hundred or ten spot, 300 and 350 are much easier to compute in our heads.<\/p>\n

Guided Practice<\/strong><\/p>\n

Do You Understand?<\/strong><\/p>\n

Question 1.
\nNumber Sense<\/strong> Leo is estimating 53.1 \u00f7 8.4. Do you think he should use 53 \u00f7 8 or 54 \u00f7 9 to estimate? Why?
\nAnswer:
\nEstimate 53.1 \u00f7 8.4. Use compatible numbers.
\nLook for compatible numbers.
\n53.1 \u00f7 8.4 is close to 54 \u00f7 9 = 6.
\n53 \u00f7 8 is not easy to find and 54 \u00f7 9 is easy to find because 54 is multiple of 9.
\nExplanation:
\nCompatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 53.1 \u00f7 8.4 is closes to 54 \u00f7 9. The actual dividend 53.1 is compatible to 54. Perform division operation 54 \u00f7 9 = 6. The Estimated quotient is 6. Here 54 is multiple of 9 so we can easily find out the quotient. 53 \u00f7 8 = 6.625 so it is difficult to find.<\/p>\n

Question 2.
\nIs each quotient greater than or less than 1?
\nA. 0.2 \u00f7 4
\nB. 1.35 \u00f7 0.6
\nAnswer:
\nA. 0.2 \u00f7 4 = 0.05
\n0.05 < 1
\nB. 1.35 \u00f7 0.6 = 2.25
\n2.25 > 1
\nExplanation:
\nA. Divide 0.2 by 4 then the quotient is 0.05. 0.05 is less than 1.
\nB. Divide 1.35 by 0.6 then the quotient is 2.25. 2.25 is greater than 1.<\/p>\n

How do you know?<\/strong><\/p>\n

In 3-8, estimate each quotient. Use rounding or compatible numbers.<\/p>\n

Question 3.
\n42 \u00f7 6.8
\nAnswer:
\nEstimate 42 \u00f7 6.8. Use compatible numbers.
\nLook for compatible numbers.
\n42 \u00f7 6.8 is closes to 42 \u00f7 7 = 6.
\nThe Estimated quotient is 6.
\nExplanation:
\nCompatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 42 \u00f7 6.8 is closes to 42 \u00f7 7. The actual divisor 6.8 is compatible to 7. Perform division operation 42 \u00f7 7 = 6. The Estimated quotient is 6.<\/p>\n

Question 4.
\n102 \u00f7 9.6
\nAnswer:
\nEstimate 102 \u00f7 9.6. Use rounding.
\nRound to the nearest ten: 102 rounds to 100; 9.6 rounds to 10
\n102 \u00f7 9.6 is about 100 \u00f7 10 = 10.
\nExplanation:
\nRounding means replacing a number with an approximate value. In the above division method 102 \u00f7 9.6. Round the numbers to the nearest ten or hundreds. Here 102 is rounded to 100 and 9.6 is rounded to 10. Now perform division operation on 100 \u00f7 10 = 10. The estimated quotient is 10.<\/p>\n

Question 5.
\n48.9 \u00f7 4
\nAnswer:
\nEstimate 48.9 \u00f7 4. Use compatible numbers.
\nLook for compatible numbers.
\n48.9 \u00f7 4 is closes to 50 \u00f7 5 = 10.
\nThe Estimated quotient is 10.
\nExplanation:
\nCompatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 48.9 \u00f7 4 is closes to 50 \u00f7 5. The actual dividend is 48.9 is compatible to 50. The actual divisor 4 is compatible to 5. Perform division operation 50 \u00f7 5 =10. The Estimated quotient is 10.<\/p>\n

Question 6.
\n72.59 \u00f7 7
\nAnswer:
\nEstimate 72.59 \u00f7 7. Use rounding.
\nRound to the nearest ten: 72.59 rounds to 70; 7 rounds to 10
\n72.59 \u00f7 7 is about 70 \u00f7 10 = 7.
\nExplanation:
\nRounding means replacing a number with an approximate value. In the above division method 72.59 \u00f7 7. Round the numbers to the nearest ten or hundreds. Here 72.59 is rounded to 70 and 7 is rounded to 10. Now perform division operation on 70 \u00f7 10 = 7. The estimated quotient is 7.<\/p>\n

Question 7.
\n15.4 \u00f7 1.9
\nAnswer:
\nEstimate 15.4 \u00f7 1.9. Use compatible numbers.
\nLook for compatible numbers.
\n15.4 \u00f7 1.9 is closes to 16 \u00f7 2 = 8.
\nThe Estimated quotient is 8.
\nExplanation:
\nCompatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 15.4 \u00f7 1.9 is closes to 16 \u00f7 2. The actual dividend is 15.4 is compatible to 16. The actual divisor 1.9 is compatible to 2. Perform division operation 16 \u00f7 2 =8. The Estimated quotient is 8.<\/p>\n

Question 8.
\n44.07 \u00f7 6.3
\nAnswer:
\nEstimate 44.07 \u00f7 6.3. Use compatible numbers.
\nLook for compatible numbers.
\n44.07 \u00f7 6.3 is closes to 42 \u00f7 6 = 7.
\nThe Estimated quotient is 7.
\nExplanation:
\nCompatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 44.07 \u00f7 6.3 is closes to 42 \u00f7 6. The actual dividend is 44.07 is compatible to 42. The actual divisor 6.3 is compatible to 6. Perform division operation 42 \u00f7 6 =7. The Estimated quotient is 7.<\/p>\n

Independent Practice<\/strong><\/p>\n

Leveled Practice<\/strong> In 9 and 10, complete the work to estimate each quotient.<\/p>\n

Question 9.
\n\"Envision
\nAnswer:
\nEstimate 64.5 \u00f7 12.3. Use rounding.
\nRound to the nearest ten: 64.5 rounds to 65 ; 12.3 rounds to 10
\n64.5 \u00f7 12.3 is about 65 \u00f7 10 = 6.5.
\nExplanation:
\nRounding means replacing a number with an approximate value. In the above division method 64.5 \u00f7 12.3. Round the numbers to the nearest ten or hundreds. Here 64.5 is rounded to 65 and 12.3 is rounded to 10. Now perform division operation on 65 \u00f7 10 = 6.5. The estimated quotient is 6.5.<\/p>\n

Question 10.
\nEstimate 64.5 \u00f7 12.3 using compatible numbers.
\n65 \u00f7 10 = _____
\nAnswer:
\nEstimate 64.5 \u00f7 12.3. Use compatible numbers.
\nLook for compatible numbers.
\n64.5 \u00f7 12.3 is closes to 65 \u00f7 10 = 6.5.
\nThe Estimated quotient is 6.5.
\nExplanation:
\nCompatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 64.5 \u00f7 12.3 is closes to 65 \u00f7 10. The actual dividend is 64.5 is compatible to 65. The actual divisor 12.3 is compatible to 10. Perform division operation 65 \u00f7 10 =6.5. The Estimated quotient is 6.5.<\/p>\n

In 11-19, estimate each quotient.<\/p>\n

Question 11.
\n7 \u00f7 0.85
\nAnswer:
\nEstimate 7 \u00f7 0.85. Use compatible numbers.
\nLook for compatible numbers.
\n7 \u00f7 0.85 is closes to 7 \u00f7 1 = 7.
\nThe Estimated quotient is 7.
\nExplanation:
\nCompatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 7 \u00f7 0.85 is closes to 7 \u00f7 1. The actual divisor 0.85 is compatible to 1. Perform division operation 7 \u00f7 1 = 7. The Estimated quotient is 7.<\/p>\n

Question 12.
\n9.6 \u00f7 0.91
\nAnswer:
\nEstimate 9.6 \u00f7 0.91. Use compatible numbers.
\nLook for compatible numbers.
\n9.6 \u00f7 0.91 is closes to 10 \u00f7 1 = 10.
\nThe Estimated quotient is 10.
\nExplanation:
\nCompatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 9.6 \u00f7 0.91 is closes to 10 \u00f7 1. The actual dividend 9.6 is compatible to 10.The actual divisor 0.91 is compatible to 1. Perform division operation 10 \u00f7 1 = 10. The Estimated quotient is 10.<\/p>\n

Question 13.
\n17.7 \u00f7 3.2
\nAnswer:
\nEstimate 17.7 \u00f7 3.2. Use compatible numbers.
\nLook for compatible numbers.
\n17.7 \u00f7 3.2 is closes to 18 \u00f7 3 = 6.
\nThe Estimated quotient is 6.
\nExplanation:
\nCompatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 17.7 \u00f7 3.2 is closes to 18 \u00f7 3. The actual dividend 17.7 is compatible to 18.The actual divisor 3.2 is compatible to 3. Perform division operation 18 \u00f7 3 = 6. The Estimated quotient is 6.<\/p>\n

Question 14.
\n91.02 \u00f7 4.9
\nAnswer:
\nEstimate 91.02 \u00f7 4.9. Use compatible numbers.
\nLook for compatible numbers.
\n91.02 \u00f7 4.9 is closes to 90 \u00f7 5 = 18.
\nThe Estimated quotient is 18.
\nExplanation:
\nCompatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 91.02 \u00f7 4.9 is closes to 90 \u00f7 5. The actual dividend 91.02 is compatible to 90.The actual divisor 4.9 is compatible to 5. Perform division operation 90 \u00f7 5 = 18. The Estimated quotient is 18.<\/p>\n

Question 15.
\n45.64 \u00f7 6.87
\nAnswer:
\nEstimate 45.64 \u00f7 6.87. Use compatible numbers.
\nLook for compatible numbers.
\n45.64 \u00f7 6.87 is closes to 49 \u00f7 7 = 7.
\nThe Estimated quotient is 7.
\nExplanation:
\nCompatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 45.64 \u00f7 6.87 is closes to 49 \u00f7 7. The actual dividend 45.64 is compatible to 49.The actual divisor 6.87 is compatible to 7. Perform division operation 49 \u00f7 7 = 7. The Estimated quotient is 7.<\/p>\n

Question 16.
\n821.22 \u00f7 79.4
\nAnswer:
\nEstimate 821.22 \u00f7 79.4. Use rounding.
\nRound to the nearest ten: 821.22 rounds to 800 ; 79.4 rounds to 80
\n821.22 \u00f7 79.4 is about 800 \u00f7 80 = 10.
\nExplanation:
\nRounding means replacing a number with an approximate value. In the above division method 821.22 \u00f7 79.4. Round the numbers to the nearest ten or hundreds. Here 821.22 is rounded to 800 and 79.4 is rounded to 80. Now perform division operation on 800 \u00f7 80 = 10. The estimated quotient is 10.<\/p>\n

Question 17.
\n22.5 \u00f7 3
\nAnswer:
\nEstimate 22.5 \u00f7 3. Use compatible numbers.
\nLook for compatible numbers.
\n22.5 \u00f7 3 is closes to 24 \u00f7 3 = 8.
\nThe Estimated quotient is 8.
\nExplanation:
\nCompatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 22.5 \u00f7 3 is closes to 24 \u00f7 3. The actual dividend 22.5 is compatible to 24. Perform division operation 24 \u00f7 3 = 8. The Estimated quotient is 8.<\/p>\n

Question 18.
\n15.66 \u00f7 9.3
\nAnswer:
\nEstimate 15.66 \u00f7 9.3. Use rounding.
\nRound to the nearest ten: 15.66 rounds to 20 ; 9.3 rounds to 10.
\n15.66 \u00f7 9.3 is about 20 \u00f7 10 = 2.
\nExplanation:
\nRounding means replacing a number with an approximate value. In the above division method 15.66 \u00f7 9.3. Round the numbers to the nearest ten or hundreds. Here 15.66 is rounded to 20 and 9.3 is rounded to 10. Now perform division operation on 20 \u00f7 10 = 2. The estimated quotient is 2.<\/p>\n

Question 19.
\n156.3 \u00f7 14.5
\nAnswer:
\nEstimate 156.3 \u00f7 14.5. Use rounding.
\nRound to the nearest ten: 156.3 rounds to 160 ; 14.5 rounds to 20.
\n156.3 \u00f7 14.5 is about 160 \u00f7 20 = 8.
\nExplanation:
\nRounding means replacing a number with an approximate value. In the above division method 156.3 \u00f7 14.5. Round the numbers to the nearest ten or hundreds. Here 156.3 is rounded to 160 and 14.5 is rounded to 20. Now perform division operation on 160 \u00f7 20 = 8. The estimated quotient is 8.<\/p>\n

Problem Solving<\/strong><\/p>\n

Question 20.
\nLuci’s mother gave her $7.50 to buy 8 spiral notebooks. With tax, the cost of each notebook is $1.05. Does Luci have enough money? Use compatible numbers and estimation to help you decide.
\nAnswer:<\/p>\n

Question 21.
\nCritique Reasoning<\/strong> Kerri said that the quotient of 4.2 \u00f7 5 is about 8 tenths because 4.2 \u00f7 5 is close to 40 tenths \u00f7 5. Do you agree with Kerri’s reasoning? Explain.
\nAnswer:<\/p>\n

Question 22.
\nHigher Order Thinking<\/strong> Write a decimal division problem that has an estimated quotient of 4. Explain how to get that estimate.
\nAnswer:<\/p>\n

Question 23.
\nLia’s car averages 14.5 miles per gallon while Roman’s car averages 28.5 miles per gallon. Use estimation to find how many times as many miles per gallon Roman’s car gets compared to Lia’s car.
\nAnswer:<\/p>\n

In 24-26, use the table.<\/p>\n

\"Envision<\/p>\n

Question 24.
\nenVision\u00ae STEM<\/strong> Which sample from the experiment had the least mass? Which had the lowest temperature?
\nAnswer:
\nIn the above table we can observe Sample 3 had the least mass 0.058 g from the experiment. Sample 1 had the lowest temperature as 37.57\u00b0C.<\/p>\n

Question 25.
\nSample 3 was used in another experiment. A temperature of 82.14\u00b0C was recorded. How many degrees did the temperature change?
\nAnswer:
\nIn the above table we can observe sample 3 had the temperature 75.50\u00b0C. Sample 3 was used in another experiment. A temperature of 82.14\u00b0C was recorded. The difference of these two temperatures are 6.64\u00b0C<\/p>\n

Question 26.
\nWhat is the difference in mass between Sample 1 and Sample 2?
\nAnswer:
\nSample 1 has the mass 0.98 g.
\nSample 2 has the mass 0.58 g.
\nThe difference in mass between Sample 1 and Sample 2 is 0.4.<\/p>\n

Assessment Practice<\/strong><\/p>\n

Question 27.
\nMauricio scored a total of 34.42 points in five gymnastic events. Which equation shows the best way to estimate Mauricio’s score for each event?
\nA. 35 \u00f7 5 = 7
\nB. 35 \u00f7 7 = 5
\nC. 30 \u00f7 10 = 3
\nD. 40 \u00f7 10 = 4
\nAnswer:
\nOption A 35 \u00f7 5 = 7 is correct.
\n35 \u00f7 5 = 7 is the best way to estimate Mauricio’s score for each event.
\nExplanation:
\nMauricio scored a total of 34.42 points in five gymnastic events. Use compatible method. In the above options option A is correct. The equation 34.42 \u00f7 5 is closes to 35 \u00f7 5. The actual dividend 34.42 is compatible to 35. Perform division operation 35 \u00f7 5 = 7. The Estimated score for each event is 8.<\/p>\n

Question 28.
\nTerry paid $117.50 for 18 identical flash drives. Which is the best estimate for the cost of each flash drive?
\nA. $6
\nB. $10
\nC. $12
\nD. $60
\nAnswer:
\nOption A $6 is correct.
\n$117.50 \u00f7 18
\n$120 \u00f7 20 = $6.
\nThe estimated cost of each flash drive is 6.
\nExplanation:
\nTerry paid $117.50 for 18 identical flash drives. Use rounding method. Rounding means replacing a number with an approximate value. In the above division method $117.50 \u00f7 18. Round the numbers to the nearest ten or hundreds. Here $117.50 is rounded to $120 and 18 is rounded to 20. Now perform division operation on $120 \u00f7 20 = $6. The estimated cost of each flash drive is $6.<\/p>\n

Lesson 6.3 Use Models to Divide by a 1-Digit Whole Number<\/h3>\n

Activity<\/strong><\/p>\n

Solve&Share<\/strong>
\nChris paid $3.60 for 3 colored pens. Each pen costs the same amount. How much did each pen cost? Solve this problem any way you choose.<\/p>\n

You can use appropriate tools such as drawings, money, or place-value blocks to help you divide. Show your work!
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-30\"
\nEach pen cost is $1.20.
\nExplanation:
\nChris paid $3.60 for 3 colored pens. Each pen costs the same amount. Divide $3.60 with 3 colored pens then the quotient is $1.20. Each pen cost is $1.20.<\/p>\n

Look Back!<\/strong> Without dividing, how do you know that the answer to the problem above must be greater than 1?
\nAnswer:
\nThe answer to the above problem must be greater than 1. Because each pen costs the same amount. we can clearly see that Chris paid $3.60 for 3 colored pens. So we can say without dividing method the answer to the above problem is greater than 1<\/p>\n

Visual Learning Bridge<\/strong><\/p>\n

Essential Question<\/strong> How Can You Use Models to Find a Decimal Quotient?<\/p>\n

A.<\/strong>
\nThree friends received $2.58 for aluminum cans they recycled. They decided to share the money equally. How much will each friend get?<\/p>\n

You can use place value blocks. Let a 100 square = $1.00, a tenth bar = $0.10, and a hundredth cube = $0.01.
\n\"Envision
\nFind 2.58 \u00f7 3.
\n\"Envision<\/p>\n

B.<\/strong>
\nThere are not enough ones to put 1 in each group, so regroup the 2 ones into 20 tenths. You can see that there are 25 tenths in 2.58. Divide the 25 tenths into 3 equal groups.
\n\"Envision<\/p>\n

C.<\/strong>
\nTrade the one extra tenth for 10 hundredths to get 18 hundredths. Divide the 18 hundredths into 3 equal groups. Each group gets 6 hundredths.
\n\"Envision
\nEach of the 3 friends will get $0.86.<\/p>\n

Convince Me! Reasoning<\/strong> The next week, 4 friends got $8.24 for the cans they collected. How much money will each friend get? Estimate using compatible numbers and then use a strategy to find the answer.<\/p>\n

Guided Practice<\/strong><\/p>\n

Do You Understand?<\/strong><\/p>\n

Question 1.
\nWhat is a reasonable estimate for 8.24 \u00f7 4? Explain.
\nAnswer:
\nEstimate $8.24 \u00f7 4. Use compatible numbers.
\nLook for compatible numbers.
\n$8.24 \u00f7 4 is closes to $8 \u00f7 4 = $2.
\nThe Estimated quotient is $2.
\nEach friend get $2.
\nExplanation:
\nCompatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. The next week, 4 friends got $8.24 for the cans they collected. In the above division problem $8.24 \u00f7 4 is closes to 8 \u00f7 4. The actual dividend 8.24 is compatible to 8. Perform division operation 8 \u00f7 4 = 2. The Estimated quotient is 2. Each friend get $2.<\/p>\n

Question 2.
\nHow is dividing a decimal by a whole number similar to dividing a whole number by a whole number? Explain.
\nAnswer:<\/p>\n

Do You Know How?<\/strong><\/p>\n

Question 3.
\nUse models to help you divide 2.16 \u00f7 4. Complete the division calculation.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-30.6\"
\n2.16 \u00f7 4 = 0.54.
\nExplanation:
\nIn the above image we can observe the division of 2.16 \u00f7 4 = 0.54. There are not enough ones to put 1 in each group, so regroup the 2 ones into 20 tenths. Divide 20 tenths into 4 equal groups. Each group gets 5 tenths. Four groups of 0.5 = 2.0.
\nTrade the one extra tenth for 10 hundredths to get 16 hundredths. Divide the 16 hundredths into 4 equal groups. Each group gets 4 hundredths. Four groups of 0.04 = 0.16.<\/p>\n

Independent Practice<\/strong><\/p>\n

Leveled Practice<\/strong> In 4-9, divide. Use or draw models to help.<\/p>\n

Question 4.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-30.7\"
\n1.35 \u00f7 3 = 0.45
\nExplanation:
\nIn the above image we can observe the division of 1.35 \u00f7 3 = 0.45. There are not enough ones to put 1 in each group, so regroup the 1 ones into 10 tenths. We can see that there are 13 tenths in 1.35. Divide the 13 tenths into 3 equal groups. Each group gets 4 tenths. Three groups of 0.4 = 1.2.
\nTrade the one extra tenth for 10 hundredths to get 15 hundredths. Divide the 15 hundredths into 3 equal groups. Each group gets 5 hundredths. Three groups of 0.05 = 0.15.<\/p>\n

Question 5.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-30.8\"
\n5.72 \u00f7 4 = 1.43
\nExplanation:
\nIn the above image we can observe the division of 5.72 \u00f7 4 = 1.43. There are enough ones to put 1 in each group, and extra ones is regrouped. Divide the 5 ones into 4 equal groups. Each group gets 1 ones. Four groups of 1 = 4. Regroup of the 1 ones into 10 tenths. We can see that there are 17 tenths in 5.72. Divide the 17 tenths into 4 equal groups. Each group gets 4 tenths. Four groups of 0.4 = 1.6.
\nTrade the one extra tenth for 10 hundredths to get 12 hundredths. Divide the 12 hundredths into 4 equal groups. Each group gets 3 hundredths. Four groups of 0.03 = 0.12.<\/p>\n

Question 6.
\n2.38 \u00f7 7
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-30.9\"
\n2.38 \u00f7 7 = 0.34.
\nExplanation:
\nIn the above image we can observe the division of 2.38 \u00f7 7 = 0.34. There are not enough ones to put 1 in each group, so regroup the 2 ones into 20 tenths. We can see that there are 23 tenths in 2.38. Divide the 23 tenths into 7 equal groups. Each group gets 3 tenths. Seven groups of 0.3 = 2.1.
\nTrade the two extra tenth for 20 hundredths to get 28 hundredths. Divide the 28 hundredths into 7 equal groups. Each group gets 4 hundredths. Seven groups of 0.04 = 0.28.<\/p>\n

Question 7.
\n4.71 \u00f7 3
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-30.10\"
\n4.71 \u00f7 3 = 1.57.
\nExplanation:
\nIn the above image we can observe the division of 4.71 \u00f7 3 = 1.57. There are enough ones to put 1 in each group, and extra ones is regrouped. Divide the 3 ones into 3 equal groups. Each group gets 1 ones. Three groups of 1 = 3. Regroup of the 1 ones into 10 tenths. We can see that there are 17 tenths in 4.71. Divide the 17 tenths into 3 equal groups. Each group gets 5 tenths. Three groups of 0.5 = 1.5.
\nTrade the two extra tenth for 20 hundredths to get 21 hundredths. Divide the 21 hundredths into 3 equal groups. Each group gets 7 hundredths. Three groups of 0.07 = 0.21.<\/p>\n

Question 8.
\n1.76 \u00f7 8
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-30.11\"
\n1.76 \u00f7 8 = 0.22.
\nExplanation:
\nIn the above image we can observe the division of 1.76 \u00f7 8 = 0.22. There are not enough ones to put 1 in each group, so regroup the 1 ones into 10 tenths. We can see that there are 17 tenths in 1.76. Divide the 17 tenths into 8 equal groups. Each group gets 2 tenths. Eight groups of 0.2 = 1.6.
\nTrade the one extra tenth for 10 hundredths to get 16 hundredths. Divide the 16 hundredths into 8 equal groups. Each group gets 2 hundredths. Eight groups of 0.02 = 0.16.<\/p>\n

Question 9.
\n5.36 \u00f7 2
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-30.12\"
\n5.36 \u00f7 2 = 2.68.
\nExplanation:
\nIn the above image we can observe the division of 5.36 \u00f7 2 = 2.68. There are enough ones to put 2 in each group, and extra ones is regrouped. Divide the 5 ones into 2 equal groups. Each group gets 2 ones. Two groups of 2 = 4. Regroup of the 1 ones into 10 tenths. We can see that there are 13 tenths in 5.36. Divide the 13 tenths into 2 equal groups. Each group gets 6 tenths. Two groups of 0.6 = 1.2.
\nTrade the one extra tenth for 10 hundredths to get 16 hundredths. Divide the 16 hundredths into 2 equal groups. Each group gets 8 hundredths. Two groups of 0.08 = 0.16.<\/p>\n

Problem Solving<\/strong><\/p>\n

Question 10.
\nReasoning<\/strong> Alan is modeling 2.65 \u00f7 5. How should he exchange the place-value blocks so he can make 5 equal shares?
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-30.13\"
\n2.65 \u00f7 5 = 0.53
\nExplanation:
\nIn the above image we can observe the division of 2.65 \u00f7 5 = 0.53. There are not enough ones to put 1 in each group, so regroup the 2 ones into 20 tenths. We can see that there are 26 tenths in 2.65. Divide the 26 tenths into 5 equal groups. Each group gets 5 tenths. Five groups of 0.5 = 2.5.
\nTrade the one extra tenth for 10 hundredths to get 15 hundredths. Divide the 15 hundredths into 5 equal groups. Each group gets 3 hundredths. Five groups of 0.03 = 0.15.<\/p>\n

Question 11.
\nAlgebra<\/strong> Abby wants to know the value of n in the equation 7.913 \u00d7 n = 791.3. What value for n makes the equation true?
\nAnswer:
\n7.913 \u00d7 n = 791.3
\n7.913 \u00d7 100 = 791.3
\nIf n= 100 makes the equation true.<\/p>\n

Question 12.
\nTo find 5.16 \u00f7 6, should you divide the ones first or the tenths first? Why?
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-30.14\"
\nFirst we have to divide the ones first.
\n5.16 \u00f7 6 = 0.86
\nExplanation:
\nIn the above image we can observe the division of 5.16 \u00f7 6 = 0.86. There are not enough ones to put 1 in each group, so regroup the 5 ones into 50 tenths. We can see that there are 51 tenths in 5.16. Divide the 51 tenths into 6 equal groups. Each group gets 8 tenths. Six groups of 0.8 = 4.8.
\nTrade the one extra tenth for 10 hundredths to get 36 hundredths. Divide the 36 hundredths into 6 equal groups. Each group gets 6 hundredths. Six groups of 0.06 = 0.36.<\/p>\n

Question 13.
\nThere are 264 children going on a field trip. Are 5 buses enough if each bus holds 52 children? Tell how you decided.
\nAnswer:
\n264 \u00f7 5 = 52.8
\n5 buses are not enough to hold 52 children in each bus.
\nExplanation:
\nThere are 264 children going on a field trip. Divide 264 by 5 then the quotient is 52.8. 5 buses are not enough to hold 52 children in each bus.<\/p>\n

Question 14.
\nHigher Order Thinking<\/strong> Ginny earned $49.50 for 6 hours of gardening and $38.60 for 4 hours of babysitting. For which job did she earn more money per hour? How much more per hour did she earn? Explain how you found the answers.<\/p>\n

Think about what information in the problem you need to compare.
\n\"Envision
\nAnswer:
\nGinny earned $49.50 for 6 hours of gardening.
\n$49.50 \u00f7 6 = $8.25.
\nGinny earns $8.25 per hour.
\nGinny earned $38.60 for 4 hours of babysitting.
\n$38.60 \u00f7 4 = $9.65.
\nGinny earns $9.65 per hour.
\n$9.65 – $8.25 = $1.4.
\nShe earns more $1.4 per hour.
\nExplanation:
\nGinny earned $49.50 for 6 hours of gardening. Perform division operation on $49.50 \u00f7 6 = $8.25. Ginny earns $8.25 per hour. Ginny earned $38.60 for 4 hours of babysitting. Perform division operation on $38.60 \u00f7 4 = $9.65. Ginny earns $9.65 per hour. Now we have to calculate how much more money she is earning. Subtract
\n$9.65 – $8.25 = $1.4. She earns more $1.4 per hour.<\/p>\n

Assessment Practice<\/strong><\/p>\n

Question 15.
\nTia drew the model below for 1.35 \u00f7 3.
\n\"Envision
\nPart A<\/strong>
\nExplain the mistake Tia made.
\nAnswer:
\n1.35 \u00f7 3 = 0.45.
\nExplanation:
\nIn the above image we can observe the 4 groups. Tia made a mistake of drawing the model above. She has to draw 3 groups. She drew one extra group of 4 tenths and 5 hundredths.
\nPart B<\/strong>
\nDraw the correct model and find the quotient.
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-30.10
\n1.35 \u00f7 3 = 0.45.
\nThe quotient is 0.45.
\nExplanation:
\nIn the above image we can observe the division of 1.35 \u00f7 3 = 0.45. There are not enough ones to put 1 in each group, so regroup the 1 ones into 10 tenths. We can see that there are 13 tenths in 1.35. Divide the 13 tenths into 3 equal groups. Each group gets 4 tenths. Three groups of 0.4 = 1.2.
\nTrade the one extra tenth for 10 hundredths to get 15 hundredths. Divide the 15 hundredths into 3 equal groups. Each group gets 5 hundredths. Three groups of 0.05 = 0.15.<\/p>\n

Lesson 6.4 Divide by a 2-Digit Whole Number<\/h3>\n

Activity<\/strong><\/p>\n

Solve&Share<\/strong><\/p>\n

Stan has a rectangular piece of carpet with an area of 23.4 square meters. The piece of carpet is 13 meters long. What is the width of the piece of carpet? Solve this problem any way you choose.<\/p>\n

Model with Math<\/strong> You can write an equation to model the problem.
\n\"Envision<\/p>\n

Look Back!<\/strong> How could you estimate the width of the piece of carpet?
\nAnswer:
\n23.4 \u00f7 13 = ?
\n23.4 \u00f7 13 = 1.8
\nThe width of the piece of carpet is 1.8 meters.
\nExplanation:
\nStan has a rectangular piece of carpet with an area of 23.4 square meters. The piece of carpet is 13 meters long. Perform division operation 23.4 \u00f7 13 = 1.8. The width of the piece of carpet is 1.8 meters.<\/p>\n

Visual Learning Bridge<\/strong><\/p>\n

Essential Question<\/strong> How Do You Divide Decimals Question by 2-Digit Numbers?<\/p>\n

A.<\/strong>
\nErin’s garden has an area of 84.8 square feet. She knows the length is 16 feet. What is the width of Erin’s garden? How can you solve 84.8 \u00f7 16 = w?
\n\"Envision<\/p>\n

You can use what you know about dividing whole numbers to help.
\n\"Envision<\/p>\n

B.<\/strong>
\nThe total area is 84.8. The pieces of the model represent the areas for the partial quotients.
\n\"Envision<\/p>\n

Convince Me! Reasoning<\/strong> How could Amy use estimation to make sure the decimal point is in the correct place in the quotient?<\/p>\n

Guided Practice<\/strong><\/p>\n

Do You Understand?<\/strong>
\nIn 1 and 2, use the example on the previous page.<\/p>\n

Question 1.
\nWhere is 5.3 shown in the diagram?
\nAnswer:<\/p>\n

Question 2.
\nHow can you check that the quotient 5.3 is reasonable? Explain.
\nAnswer:<\/p>\n

Do You Know How?<\/strong><\/p>\n

In 3 and 4, complete the division problem.<\/p>\n

Question 3.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-40.1\"
\n306.25 \u00f7 49 = 6.25
\nExplanation:
\nIn the above image we can observe the division operation\u00a0 306.25 \u00f7 49 = 6.25. The nearest possible multiple value of 49 is 294(49 x 6). Subtract 294 from 306.25 so as to get the remainder 12.25. 49 cannot be a multiple of 12.25 and so we have kept a decimal in the quotient and now 49 has the least possible multiple value of 9.8(49 x 0.2) near to 12.25. After subtracting 9.8 from 12.25, we are now having 6.2 as quotient and 2.45 as remainder. Now the possible multiple value of 49 near to 2.45 is 2.45 itself(49 x 0.05 = 2.45). Now the remainder is zero and the final quotient is 6.25.<\/p>\n

Question 4.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-40.2\"
\n28.5 \u00f7 15 = 1.9
\nExplanation:
\nIn the above image we can observe the division operation\u00a0 28.5 \u00f7 15 = 1.9. The nearest possible multiple value of 15 is 15(15 x 1). Subtract 15 from 28.5 so as to get the remainder 13.5. 15 cannot be a multiple of 13.5 and so we have kept a decimal in the quotient and now the possible multiple value of 15 near to 13.5 is 13.5 itself(15 x 0.9 = 13.5). Now the remainder is zero and the final quotient is 1.9.<\/p>\n

Independent Practice<\/strong><\/p>\n

Leveled Practice<\/strong> In 5-6, find each quotient and label the model.<\/p>\n

Question 5.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-40.3\"
\n78.2 \u00f7 17 = 4.6
\nExplanation:
\nIn the above image we can observe the division operation\u00a0 78.2 \u00f7 17 = 4.6. The nearest possible multiple value of 17 is 68(17 x 4). Subtract 68 from 78.2 so as to get the remainder 10.2. 17 cannot be a multiple of 10.2 and so we have kept a decimal in the quotient and now the possible multiple value of 17 near to 10.2 is 10.2 itself(17 x 0.6 = 10.2). Now the remainder is zero and the final quotient is 4.6.<\/p>\n

Question 6.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-40.4\"
\n304.75 \u00f7 53 = 5.75
\nExplanation:
\nIn the above image we can observe the division operation\u00a0 304.75\u00f7 53 = 5.75. The nearest possible multiple value of 53 is 265(53 x 5). Subtract 265 from 304.75 so as to get he remainder 39.75. 53 cannot be a multiple of 39.75 and so we have kept a decimal in the quotient and now 53 has the least possible multiple value of 37.10(53 x 0.7) near to 39.75. After subtracting 37.10 from 39.75, we are now having 5.7 as quotient and 2.65 as remainder. Now the possible multiple value of 53 near to 2.65 is 2.65 itself(53 x 0.05 = 2.65). Now the remainder is zero and the final quotient is 5.75.<\/p>\n

In 7-10, find each quotient.<\/p>\n

Question 7.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-40.5\"
\n91.8 \u00f7 27 = 3.4
\nThe quotient is 3.4
\nExplanation:
\nIn the above image we can observe the division operation\u00a0 91.8 \u00f7 27 = 3.4. The nearest possible multiple value of 27 is 81(27 x 3). Subtract 81 from 91.8 so as to get the remainder as 10.8. 27 cannot be a multiple of 10.8 and so we have kept a decimal in the quotient and now the possible multiple value of 27 near to 10.8 is 10.8 itself(27 x 0.4 = 10.8). Now the remainder is zero and the final quotient is 3.4.<\/p>\n

Question 8.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-40.6\"
\n3.9 \u00f7 15 = 0.26
\nThe quotient is 0.26
\nExplanation:
\nIn the above image we can observe the division operation\u00a0 3.9 \u00f7 15 = 0.26. 15 cannot be a multiple of 3.9 so we have kept a decimal in the quotient and now 15 has the least possible multiple value of 3.0(15 x 0.2) near to 3.9. Subtract 3.0 from 3.9 then the remainder is 0.9.\u00a0 Now the possible multiple value of 15 near to 0.9 is 0.9 itself(15 x 0.06 = 0.9). Now the remainder is zero and the final quotient is 0.26.<\/p>\n

Question 9.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-40.7\"
\n39.6 \u00f7 12 = 3.3
\nThe quotient is 3.3
\nExplanation:
\nIn the above image we can observe the division operation\u00a0 39.6 \u00f7 12 = 3.3. The nearest possible multiple value of 12 is 36(12 x 3). Subtract 36 from 39.6 so as to get the remainder as 3.6. 12 cannot be a multiple of 3.6 and so we have kept a decimal in the quotient and now the possible multiple value of 12 near to 3.6 is 3.6 itself(12 x 0.3 = 3.6). Now the remainder is zero and the final quotient is 3.3.<\/p>\n

Question 10.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-40.8\"
\n247.5 \u00f7 50 = 4.95
\nExplanation:
\nIn the above image we can observe the division operation\u00a0 247.5 \u00f7 50 = 4.95. The nearest possible multiple value of 50 is 200(50 x 4). Subtract 200 from 247.5 so as to get the remainder 47.5. 50 cannot be a multiple of 47.5 and so we have kept a decimal in the quotient and now 50 has the least possible multiple value of 45.0(50 x 0.9) near to 47.5. After subtracting 45.0 from 47.5, we are now having 4.9 as quotient and 2.5 as remainder. Now the possible multiple value of 50 near to 2.5 is 2.5 itself(50 x 0.05 = 2.5). Now the remainder is zero and the final quotient is 4.95.<\/p>\n

Problem Solving<\/strong><\/p>\n

Question 11.
\nSharon pays $98.75 for twenty-five 14-ounce boxes of Yummy Flakes cereal. How much does one box of cereal cost?
\nAnswer:<\/p>\n

Question 12.
\nJavier bought a new TV for $479.76. He will make equal payments each month for 2 years. How can Javier use compatible numbers to estimate each payment?
\nAnswer:
\nEstimate $479.76 \u00f7 24. Use compatible numbers.
\nLook for compatible numbers.
\n$479.76 \u00f7 24 is closes to $480 \u00f7 24 = $20.
\nThe Estimated quotient is $20.
\nJavier pays each month $20.
\nExplanation:
\nCompatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. Javier bought a new TV for $479.76. He will make equal payments each month for 2 years. 2years means 24 months. In the above division problem $479.76 \u00f7 24 is closes to 480 \u00f7 24. The actual dividend $479.76 is compatible to 480. Perform division operation 480 \u00f7 24 = 20. The Estimated quotient is 20. Javier pays each month $20.<\/p>\n

Question 13.
\nHigher Order Thinking<\/strong> The area of the rectangular flower bed shown is 20.4 square meters. How many meters of edging are needed to go around the flower bed? Explain.
\n\"Envision
\nAnswer:<\/p>\n

Question 14.
\nMake Sense and Persevere<\/strong> Ms. Wang is shopping for a new refrigerator. Brand A costs $569 and uses 635 kilowatt-hours per year. Brand B costs $647 and uses 582 kilowatt-hours per year. If electricity costs $0.18 per kilowatt-hour, how much would Ms. Wang save on electricity per year by buying Brand B?
\nAnswer:<\/p>\n

Question 15.
\nPat is driving from Seattle to Los Angeles. The distance is 1,135 miles. For the first 250 miles, it costs Pat $0.29 a mile to drive. After that, her driving cost is $0.16 a mile. What is Pat’s total driving cost?
\nAnswer:<\/p>\n

Assessment Practice<\/strong><\/p>\n

Question 16.
\nWhich is equal to 27.3 divided by 13?
\nA. 0.21
\nB. 2.01
\nC. 2.1
\nD. 21
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-40.9\"
\n27.3 \u00f7 13 = 2.1
\nOption C is correct.
\nExplanation:
\nDivide 27.3 by 13 then the quotient is 2.1. So option C is correct.<\/p>\n

Question 17.
\nWhich is equal to 73.5 divided by 21?
\nA. 0.35
\nB. 3.05
\nC. 3.5
\nD. 30.5
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals-40.10\"
\n73.5 \u00f7 21 = 3.5
\nOption C is correct.
\nExplanation:
\nDivide 73.5 by 21 the quotient is 3.5. So option C is correct.<\/p>\n

Lesson 6.5 Divide by a Decimal<\/h3>\n

Activity<\/strong><\/p>\n

Solve & Share<\/strong>
\nAaron buys erasers for his pencils. Each eraser costs $0.20. The total cost is $1.20. How many erasers does Aaron buy? Solve this problem any way you choose.<\/p>\n

You can model the problem using hundredth grids or other drawings. Show your work!
\n\"Envision<\/p>\n

Look Back! Reasoning<\/strong> How do you know your answer makes sense?
\nAnswer:
\n$1.20 \u00f7 ? = $0.20
\n$1.20 \u00f7 6 = $0.20
\nAaron buys 6 erasers for his pencils.
\nExplanation:
\nAaron buys erasers for his pencils. Each eraser costs $0.20. The total cost is $1.20. Divide $1.20 by $0.20 then the answer is 6. Aaron buys 6 erasers for his pencils.<\/p>\n

Visual Learning Bridge<\/strong><\/p>\n

Essential Question<\/strong> How Can You Divide a Preston Decimal by a Decimal?<\/p>\n

A.<\/strong>
\nMichelle purchases several bottles of water. Before tax is added, the total cost is $3.60 and the cost of each bottle is $1.20. How many bottles did she buy?
\nDivide $3.60 by $1.20.
\n\"Envision<\/p>\n

You can use what you know about division with whole numbers to find how many groups of $1.20 are in $3.60.
\n\"Envision<\/p>\n

B.<\/strong>
\nOne Way<\/strong>
\nThink: $3.60 is the same as 36 dimes. $1.20 is the same as 12 dimes.
\n\"Envision
\nHow many 12s are in 36?
\n\"Envision
\nShe bought 3 bottles.<\/p>\n

C.<\/strong>
\nAnother Way<\/strong>
\nThink multiplication:
\nTo find 3.60 \u00f7 1.20, use the relationship between multiplication and division.
\n1.20 \u00d7 ? = 3.60
\nWriting this another way:
\n120 hundredths \u00d7? = 360 hundredths
\n? = 3
\nShe bought 3 bottles.<\/p>\n

Convince Me! Construct Arguments<\/strong> Is 3.6 \u00f7 1.2 equal to, less than, or greater than 36 \u00f7 12? Explain.<\/p>\n

Guided Practice<\/strong><\/p>\n

Do You Understand?<\/strong><\/p>\n

Question 1.
\nHow is dividing by a decimal like dividing by a whole number?
\nAnswer:<\/p>\n

Question 2.
\nHow can you use multiplication to find 2.8 \u00f7 0.7?
\nAnswer:<\/p>\n

Do You Know How?<\/strong><\/p>\n

In 3-6, use what you know about decimal division and mental math to find each quotient.<\/p>\n

Question 3.
\n2 \u00f7 0.5
\nAnswer:
\nTo find 2 \u00f7 0.5, use the relationship between multiplication and division.
\n0.5 \u00d7 ? = 2
\n? = 4
\n2 \u00f7 0.5 = 4
\nThe quotient is 4.
\nExplanation:
\nMultiply the divisor 0.5 with 4 then the product is 2. Divide the dividend 2 with the divisor 0.5 then the quotient is 4.<\/p>\n

Question 4.
\n1.25 \u00f7 0.25
\nAnswer:
\nTo find 1.25 \u00f7 0.25, use the relationship between multiplication and division.
\n0.25 \u00d7 ? = 1.25
\n? = 5
\n1.25 \u00f7 0.25 = 5
\nThe quotient is 5.
\nExplanation:
\nMultiply the divisor 0.25 with 5 then the product is 1.25. Divide the dividend 1.25 with the divisor 0.25 then the quotient is 5.<\/p>\n

Question 5.
\n2.1 \u00f7 0.7
\nAnswer:
\nTo find 2.1 \u00f7 0.7, use the relationship between multiplication and division.
\n0.7 \u00d7 ? = 2.1
\n? = 3
\n2.1 \u00f7 0.7 = 3
\nThe quotient is 3.
\nExplanation:
\nMultiply the divisor 0.7 with 3 then the product is 1.25. Divide the dividend 2.1 with the divisor 0.7 then the quotient is 3.<\/p>\n

Question 6.
\n6.6 \u00f7 0.3
\nAnswer:
\nTo find 6.6 \u00f7 0.3, use the relationship between multiplication and division.
\n0.3 \u00d7 ? = 6.6
\n? = 3
\n6.6 \u00f7 0.3 = 22
\nThe quotient is 22.
\nExplanation:
\nMultiply the divisor 0.3 with 22 then the product is 6.6. Divide the dividend 6.6 with the divisor 0.3 then the quotient is 22.<\/p>\n

Think about how the dividend, divisor, and quotient are related.
\n\"Envision<\/p>\n

Independent Practice<\/strong><\/p>\n

In 7-10, use what you know about multiplication, division, place value, and partial quotients to divide.<\/p>\n

Question 7.
\n2.56 \u00f7 0.04
\nAnswer:
\nTo find 2.56 \u00f7 0.04, use the relationship between multiplication and division.
\n0.04 \u00d7 ? = 2.56
\nWriting this another way:
\n4 hundredths \u00d7 ? = 256 hundredths
\n? = 64
\n2.56 \u00f7 0.04 = 64
\nExplanation:
\nWe have to use the relationship between multiplication and division. Multiply the divisor 0.04 with 64 then the product is 2.56. By dividing 2.56 with 0.04 then the quotient is 64.<\/p>\n

Question 8.
\n25.6 \u00f7 0.4
\nAnswer:
\nTo find 25.6 \u00f7 0.4, use the relationship between multiplication and division.
\n0.4 \u00d7 ? = 25.6
\nWriting this another way:
\n4 tenths \u00d7 ? = 256 tenths
\n? = 64
\n25.6 \u00f7 0.4 = 64
\nExplanation:
\nWe have to use the relationship between multiplication and division. Multiply the divisor 0.4 with 64 then the product is 25.6. By dividing 25.6 with 0.4 then the quotient is 64.<\/p>\n

Question 9.
\n256 \u00f7 4
\nAnswer:
\nTo find 256 \u00f7 4, use the relationship between multiplication and division.
\n4 \u00d7 ? = 256
\nWriting this another way:
\n4 ones \u00d7 ? = 256 ones
\n? = 64
\n256 \u00f7 4 = 64
\nExplanation:
\nWe have to use the relationship between multiplication and division. Multiply the divisor 4 with 64 then the product is 256. By dividing 256 with 4 then the quotient is 64.<\/p>\n

Question 10.
\nDescribe the relationship among Problems 7, 8, and 9.
\nAnswer:
\nThe relationship among problems 7, 8, and 9. The quotient is same in all problems. In problem 7 hundredths place value is used. In problem 8 tenths place value is used. In problem 9 ones place value is used.<\/p>\n

In 11-18, find each quotient.<\/p>\n

Question 11.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-5th-Grade-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-50.1\"
\n4.75 \u00f7 0.25 = 19
\nThe quotient is 19.
\nExplanation:
\nIn this division operation 4.75 \u00f7 0.25. The dividend is 4.75 and the divisor is 0.25. By dividing dividend 4.75 with the divisor 0.25 then the quotient is 19.<\/p>\n

Question 12.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-5th-Grade-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-50.2\"
\n4.56 \u00f7 0.04 = 114
\nThe quotient is 114.
\nExplanation:
\nIn this division operation 4.56 \u00f7 0.04. The dividend is 4.56 and the divisor is 0.04. By dividing dividend 4.56 with the divisor 0.04 then the quotient is 114.<\/p>\n

Question 13.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-5th-Grade-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-50.3\"
\n1.05 \u00f7 0.05 = 21
\nThe quotient is 21.
\nExplanation:
\nIn this division operation 1.05 \u00f7 0.05. The dividend is 1.05 and the divisor is 0.05. By dividing dividend 1.05 with the divisor 0.05 then the quotient is 21.<\/p>\n

Question 14.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-5th-Grade-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-50.4\"
\n182.8 \u00f7 0.1 = 1828
\nThe quotient is 1828.
\nExplanation:
\nIn this division operation 182.8 \u00f7 0.1. The dividend is 182.8 and the divisor is 0.1. By dividing dividend 182.8 with the divisor 0.1 then the quotient is 1828.<\/p>\n

Question 15.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-5th-Grade-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-50.5\"<\/p>\n

17.25 \u00f7 0.03 = 575
\nThe quotient is 575.
\nExplanation:
\nIn this division operation 17.25 \u00f7 0.03. The dividend is 17.25 and the divisor is 0.03. By dividing dividend 17.25 with the divisor 0.03 then the quotient is 575.<\/p>\n

Question 16.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-5th-Grade-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-50.6\"
\n5.68 \u00f7 0.8 = 71
\nThe quotient is 71.
\nExplanation:
\nIn this division operation 5.68 \u00f7 0.8. The dividend is 5.68 and the divisor is 0.8. By dividing dividend 5.68 with the divisor 0.8 then the quotient is 71.<\/p>\n

Question 17.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-5th-Grade-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-50.7\"
\n6.24 \u00f7 0.06 = 104
\nThe quotient is 104.
\nExplanation:
\nIn this division operation 6.24 \u00f7 0.06. The dividend is 6.24 and the divisor is 0.06. By dividing dividend 6.24 with the divisor 0.06 then the quotient is 104.<\/p>\n

Question 18.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-5th-Grade-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-50.8\"
\n27.5 \u00f7 2.5 = 11
\nThe quotient is 11
\nExplanation:
\nIn this division operation 27.5 \u00f7 2.5. The dividend is 27.5 and the divisor is 2.5. By dividing dividend 27.5 with the divisor 2.5 then the quotient is 11.<\/p>\n

Problem Solving<\/strong><\/p>\n

Question 19.
\nMake up a money story for the equation 3.75 \u00f7 0.25 = 15.
\nAnswer:<\/p>\n

Question 20.
\nCarol bought 5 pork chops and 3 steaks. Each pork chop weighed 0.32 pound and each steak weighed 0.8 pound. How many pounds of meat did Carol buy in all?
\nAnswer:<\/p>\n

Question 21.
\nTim estimates that 60 \u00f7 5.7 is about 10. Will the actual quotient be greater than or less than 10? Explain.
\nAnswer:
\nEstimate 60 \u00f7 5.7. Use compatible numbers.
\nLook for compatible numbers.
\n60 \u00f7 5.7 is close to 60 \u00f7 6 = 10.
\nTim estimates that 60 \u00f7 5.7 is about 10.
\n60 \u00f7 5.7 = 10.53
\nThe actual quotient is 10.53.
\nExplanation:
\nCompatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 60 \u00f7 5.7 is closes to 60 \u00f7 10. The actual divisor 5.7 is compatible to 6. Perform division operation 60 \u00f7 6 = 10. The Estimated quotient is 10. The actual quotient is 10.53. The actual quotient is greater than 10.<\/p>\n

Question 22.
\nDex estimates that 4,989 \u00f7 0.89 is about 500. Is his estimate reasonable? Why or why not?
\nAnswer:
\nEstimate 4,989 \u00f7 0.89. Use compatible numbers.
\nLook for compatible numbers.
\n4,989 \u00f7 0.89 is close to 4,990 \u00f7 1 = 4,990.
\nDex estimates that 4,989 \u00f7 0.89 is about 500.
\nHis Estimation is not reasonable.
\nExplanation:
\nCompatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 4,989 \u00f7 0.89 is closes to 4,990 \u00f7 1. The actual dividend 4,989 is compatible to 4,990. The actual divisor 0.89 is compatible to 1. Perform division operation 4,990 \u00f7 1 = 4,990. The Estimated quotient is 4,990. His Estimation is not reasonable.<\/p>\n

Question 23.
\nHigher Order Thinking<\/strong> Susan solves 1.4 \u00f7 0.2 using the diagram at the right. Is her reasoning correct? Explain her thinking.
\n\"Envision
\nAnswer:<\/p>\n

Question 24.
\nUse Structure The same dividend is divided by 0.1 and 0.01. How do the quotients compare? Explain your thinking.
\nAnswer:<\/p>\n

Question 25.
\nA-Z Vocabulary<\/strong> Give three examples of a power of 10. Explain why one of your examples is a power of 10.
\nAnswer:<\/p>\n

Assessment Practice<\/strong><\/p>\n

Question 26.
\nSelect the expressions that have a quotient of 4.
\n\"Envision 2.8 \u00f7 0.7
\n\"Envision 0.28 \u00f7 7
\n\"Envision 2.8 \u00f7 0.07
\n\"Envision 0.28 \u00f7 0.07
\nAnswer:
\n\"Envision-Math-Common-Core-5th-Grade-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-52\"
\nExplanation:
\nIn the above image we can observe the expressions that have a quotient of 4. Option 1 and option 4 is correct.
\n1. When 2.8 is divided by 0.7 then the quotient is 4. So option 1 is correct.
\n2. When 0.28 is divided by 7 then the quotient is 0.04. So option 2 is not correct.
\n3. When 2.8 is divided by 0.07 then the quotient is 40. So option 3 is not correct.
\n4. When 0.28 is divided by 0.07 then the quotient is 4. So option 4 is correct.<\/p>\n

Question 27.
\nSelect the expressions that have a quotient of 9.
\n\"Envision 1.35 \u00f7 1.5
\n\"Envision 1.35 \u00f7 0.15
\n\"Envision 13.5 \u00f7 1.5
\n\"Envision 13.5 \u00f7 0.15
\nAnswer:
\n\"Envision-Math-Common-Core-5th-Grade-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-52
\nExplanation:
\nIn the above image we can observe the expressions that have a quotient of 9. Option 2 and option 3 is correct.
\n1. When 1.35 is divided by 1.5 then the quotient is 0.9. So option 1 is not correct.
\n2. When 1.35 is divided by 0.15 then the quotient is 9. So option 2 is correct.
\n3. When 13.5 is divided by 1.5 then the quotient is 9. So option 3 is\u00a0 correct.
\n4. When 13.5 is divided by 0.15 then the quotient is 90. So option 4 is not correct.<\/p>\n

Lesson 6.6 Reasoning<\/h3>\n

Activity<\/strong><\/p>\n

Problem Solving<\/strong><\/p>\n

Reasoning<\/strong><\/p>\n

Solve & Share<\/strong>
\nAaron has three slabs of beeswax. He plans to melt them and use all of the wax to form 36 candles. If all the candles are the same size and weight, how much will each candle weigh? Use reasoning to decide.<\/p>\n

\"Envision<\/p>\n

Thinking Habits<\/strong>
\nBe a good thinker! These questions can help you.
\n\u2022 What do the numbers and symbols in the problem mean?
\n\u2022 How are the numbers or quantities related?
\n\u2022 How can I represent a word problem using pictures, numbers, or equations?
\n\"Envision<\/p>\n

Look Back! Reasoning<\/strong> Suppose Aaron wants each candle to weigh 0.5 pound. How many candles could he make with the beeswax?<\/p>\n

Visual Learning Bridge<\/strong><\/p>\n

Essential Question<\/strong> How Can You Use Reasoning to Solve Problems?<\/p>\n

A.<\/strong>
\nMs. Watson is mixing mint green paint for her art class. She combines full bottles of blue, yellow, and white paint. How many 8-fluid ounce jars can she fill? Use reasoning to decide.
\n\"Envision<\/p>\n

What do I need to do to solve this problem?
\nI need to add the three quantities of paint. Then I need to divide the sum by the capacity of a jar.<\/p>\n

B.<\/strong>
\nHow can I use reasoning to solve this problem?
\nI can
\n\u2022 identify the quantities I know
\n\u2022 draw a bar diagram to show relationships.
\n\u2022 give the answer using the correct unit.<\/p>\n

Here’s my thinking…
\n\"Envision<\/p>\n

C.<\/strong>
\nUse bar diagrams to show how the quantities are related.
\nFirst, find the sum of the three quantities of paint in the mixture.
\n\"Envision
\nThen, divide 93.6 by 8 to find the 11.7 number of jars that can be filled.
\n\"Envision
\nMs. Watson can fill 11 jars. The 12th jar will be only partially filled.<\/p>\n

Convince Me! Reasoning<\/strong> Ms. Watson is mixing 34.6 fluid Ounces of red paint and 18.2 fluid ounces of yellow paint to make orange paint. How many 12-fluid Ounce jars can she fill? Use reasoning to decide.<\/p>\n

Guided Practice<\/strong><\/p>\n

Reasoning<\/strong>
\nMiranda mixed 34.5 fluid Ounces of blue paint, 40.5 fluid ounces of red paint, and 2 fluid Ounces of black paint to make purple paint. She poured the same amount of the purple paint into each of 14 jars. How much paint did she pour in each jar?<\/p>\n

Use reasoning<\/strong> to decide how the quantities in the problem are related.
\n\"Envision<\/p>\n

Question 1.
\nExplain what each of the quantities in the problem means.
\nAnswer:<\/p>\n

Question 2.
\nDescribe one way to solve the problem.
\nAnswer:<\/p>\n

Question 3.
\nWhat is the solution to the problem? Explain.
\nAnswer:<\/p>\n

Independent Practice<\/strong><\/p>\n

Reasoning<\/strong>
\nSue made chicken soup by combining the entire can of soup shown with a full can of water. How many 10-fluid Ounce bowls can she fill with the soup? How much soup will be left over?
\n\"Envision<\/p>\n

Question 4.
\nExplain what each of the quantities in the problem means.
\nAnswer:<\/p>\n

Question 5.
\nDescribe one way to solve the problem.
\nAnswer:<\/p>\n

Question 6.
\nWhat is the solution to the problem? Explain.
\nAnswer:<\/p>\n

Problem Solving<\/strong><\/p>\n

Performance Task<\/strong>
\nCooking Competition<\/strong>
\nLucas’s cooking class is having a cooking competition. There are 6 teams. Each student brought supplies that will be shared equally among the teams. The table shows the supplies Lucas brought. If the supplies are shared equally among the teams, how much of each supply will each team get?
\n\"Envision<\/p>\n

Question 7.
\nMake Sense and Persevere<\/strong> Do you need all of the information given above to solve the problem? Explain.
\nAnswer:<\/p>\n

Question 8.
\nReasoning<\/strong> Describe how to solve the problem.
\nAnswer:<\/p>\n

Use reasoning to think about what the quantities in the table represent.
\n\"Envision<\/p>\n

Question 9.
\nModel with Math<\/strong> Write equations to represent how much of each supply each team will get.
\nAnswer:<\/p>\n

Question 10.
\nBe Precise<\/strong> What is the solution to the problem? Explain.
\nAnswer:<\/p>\n

Question 11.
\nCritique Reasoning<\/strong> Lucas says that to find the total cost of the rice, you should multiply 3.5 by $1.89. Do you agree? Explain.
\nAnswer:<\/p>\n

Topic 6 Fluency Practice<\/h3>\n

Activity<\/strong><\/p>\n

Follow the path<\/strong>
\nSolve each problem. Follow products that are multiples of 20 to shade a path from START to FINISH. You can only move up, down, right, or left.
\n\"Envision<\/p>\n

\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-55.1\"
\nIn the above image we can observe some multiplication problems. Products that are multiples of 20 to shade a path from START to FINISH. The products that are shaded with green color are multiples of 20.<\/p>\n

Topic 6 Vocabulary Review<\/strong><\/p>\n

Glossary<\/strong><\/p>\n

Understand Vocabulary<\/strong><\/p>\n

Write always, sometimes, or never.<\/p>\n

Word List<\/strong>
\n\u2022 estimate
\n\u2022 exponent
\n\u2022 hundredths
\n\u2022 power
\n\u2022 quotient
\n\u2022 rounding
\n\u2022 tenths
\n\u2022 thousandths<\/p>\n

Question 1.
\nA digit in the hundredths place has \\(\\frac{1}{10}\\) the value of the same digit in the tenths place. ______
\nAnswer:
\nA digit in the hundredths place has \\(\\frac{1}{10}\\) the value of the same digit in the tenths place. Sometimes<\/strong>.<\/p>\n

Question 2.
\nThe answer to a division problem is less than the divisor. ______
\nAnswer:
\nThe answer to a division problem is less than the divisor. Sometimes<\/strong><\/p>\n

Question 3.
\nA whole number divided by a decimal number is a whole number. ____
\nAnswer:
\nA whole number divided by a decimal number is a whole number. Sometimes<\/strong><\/p>\n

Question 4.
\nDividing by 103<\/sup> moves the decimal point in the dividend three places to the left. ____
\nAnswer:
\nDividing by 103<\/sup> moves the decimal point in the dividend three places to the left. Always<\/strong><\/p>\n

Question 5.
\nMultiplying the dividend and the divisor by the same power of 10 changes the quotient. ____
\nAnswer:
\nMultiplying the dividend and the divisor by the same power of 10 changes the quotient. Never<\/strong><\/p>\n

Question 6.
\nThe answer to a division problem is greater than the divisor. ______
\nAnswer:
\nThe answer to a division problem is greater than the divisor. Sometimes<\/strong><\/p>\n

Write T for true or F for false.<\/p>\n

_____ Question 7.
\n3.65 \u00f7 5.2 < 1
\nAnswer: _____
\n3.65 \u00f7 5.2 < 1
\n0.70 < 1
\nTrue
\nExplanation:
\nPerform division operation on 3.65 \u00f7 5.2 = 0.70. The quotient is 0.70. The quotient 0.70 is less than 1. So the above expression is True.<\/p>\n

Question 8.
\n48 \u00f7 0.6 = 0.8
\nAnswer:
\n48 \u00f7 0.6 = 0.8
\n48 \u00f7 0.6 = 80
\nThe answer for above division operation is not correct.\u00a0 So the answer is False.
\nExplanation:
\nPerform division operation on 48 \u00f7 0.6 = 80. The quotient is 80.\u00a0 In the above division operation the quotient is 0.8. So the above expression is False.<\/p>\n

_____ Question 9.
\n2.42 \u00f7 2.1 > 1.
\nAnswer:
\n2.42 \u00f7 2.1 > 1.
\n1.15 > 1
\nThe answer for above division operation is 1.15 is greater than 1. So the answer is True.
\nExplanation:
\nPerform division operation on 2.42 \u00f7 2.1 = 1.15. The quotient is 1.15. The quotient 1.15 is greater than 1. So the above expression is True.<\/p>\n

_____ Question 10.
\n4.9 \u00f7 0.8 < 4.9
\nAnswer:
\n4.9 \u00f7 0.8 < 4.9
\n6.125 < 4.9
\nThe answer for above division operation is 6.125 is not less than 4.9. So the answer is False.
\nExplanation:
\nPerform division operation on 4.9 \u00f7 0.8 = 6.125. The quotient is 6.125. The quotient 6.125 is\u00a0 not less than 4.9. So the above expression is False.<\/p>\n

Use Vocabulary in Writing<\/strong><\/p>\n

Question 11.
\nMary says the digits in the quotient of 381.109 0.86 are 4 4 315, but she doesn’t know where to place the decimal point. How can Mary use number sense to place the decimal point? Use at least three terms from the Word List in your answer.
\nAnswer:<\/p>\n

Topic 6 Reteaching<\/h3>\n

Set A<\/strong>
\npages 229-232
\nFind 340.5 \u00f7 100.
\nDividing by 10, or 101<\/sup>, means moving the decimal point one place to the left.
\nDividing by 100, or 102<\/sup>, means moving the decimal point two places to the left.
\nDividing by 1,000, or 103<\/sup>, means moving the decimal point three places to the left.
\n\"Envision<\/p>\n

Remember that when dividing decimals by a power of 10, you may need to use one or more zeros as placeholders.<\/p>\n

Use mental math to find each quotient.<\/p>\n

Question 1.
\n34.6 \u00f7 101<\/sup>
\nAnswer:
\n34.6 \u00f7 101
\n<\/sup>34.6 \u00f7 10 = 3.46
\nThe quotient is 3.46.
\nExplanation:
\nDividing by 10, or 101<\/sup>, means moving the decimal point one place to the left. Move the dividend decimal point 34.6 one place to the left then the result is 3.46. The quotient is 3.46.<\/p>\n

Question 2.
\n6,483 \u00f7 102<\/sup>
\nAnswer:
\n6,483 \u00f7 102<\/sup>
\n6,483 \u00f7 100 = 64.83
\nThe quotient is 64.83.
\nExplanation:
\nDividing by 100, or 102<\/sup>, means moving the decimal point two places to the left. Move the dividend decimal point 6,483 two places to the left then the result is 64.83. The quotient is 64.83.<\/p>\n

Question 3.
\n148.3 \u00f7 100
\nAnswer:
\n148.3 \u00f7 100 = 1.483
\nThe quotient is 1.483.
\nExplanation:
\nDividing by 100, or 102<\/sup>, means moving the decimal point two places to the left. Move the dividend decimal point 148.3 two places to the left then the result is 1.483. The quotient is 1.483.<\/p>\n

Question 4.
\n29.9 \u00f7 101<\/sup>
\nAnswer:
\n29.9 \u00f7 101<\/sup>
\n29.9 \u00f7 10 = 2.99
\nThe quotient is 2.99
\nExplanation:
\nDividing by 10, or 101<\/sup>, means moving the decimal point one place to the left. Move the dividend decimal point 29.9 one place to the left then the result is 2.99. The quotient is 2.99.<\/p>\n

Question 5.
\n70.7 \u00f7 10
\nAnswer:
\n70.7 \u00f7 10 = 7.07
\nThe quotient is 7.07.
\nExplanation:
\nDividing by 10, or 101<\/sup>, means moving the decimal point one place to the left. Move the dividend decimal point 70.7 one place to the left then the result is 7.07. The quotient is 7.07.<\/p>\n

Question 6.
\n5,913 \u00f7 103<\/sup>
\nAnswer:
\n5,913 \u00f7 103<\/sup>
\n5,913 \u00f7 1000 = 5.913
\nThe quotient is 5.913.
\nExplanation:
\nDividing by 1,000, or 103<\/sup>, means moving the decimal point three places to the left. Move the dividend decimal point 5,913 three place to the left then the result is 5.913. The quotient is 5.913.<\/p>\n

Set B<\/strong>
\npages 233-236
\nEstimate 27.3 \u00f7 7.1. Use compatible numbers.
\n\"Envision
\nSo, 27.3 \u00f7 7.1 is about 4.
\nEstimate 42.5 \u00f7 11. Use rounding.
\n\"Envision
\nSo, 42.5 \u00f7 11 is about 4.<\/p>\n

Remember<\/strong> that compatible numbers are numbers that are easy to compute in your head.<\/p>\n

Write a number sentence that shows a way to estimate each quotient.<\/p>\n

Question 1.
\n26.2 \u00f7 5
\nAnswer:
\nEstimate 26.2 \u00f7 5. Use compatible numbers.
\nLook for compatible numbers.
\n26.2 \u00f7 5 is closes to 25 \u00f7 5 = 5.
\nSo, 26.2 \u00f7 5 is about 5.
\nThe Estimated quotient is 5.
\nExplanation:
\nCompatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 26.2 \u00f7 5 is closes to 25 \u00f7 5. The actual dividend 26.2 is compatible to 25. Perform division operation 25 \u00f7 5 = 5. The Estimated quotient is 5.<\/p>\n

Question 2.
\n49.6 \u00f7 7.8
\nAnswer:
\nEstimate 49.6 \u00f7 7.8. Use compatible numbers.
\nLook for compatible numbers.
\n49.6 \u00f7 7.8 is closes to 49 \u00f7 7 = 7.
\nSo, 49.6 \u00f7 7.8 is about 7.
\nThe Estimated quotient is 7.
\nExplanation:
\nCompatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 49.6 \u00f7 7.8 is closes to 49\u00f7 7. The actual dividend 49 is compatible to 25. The actual divisor 7.8 is compatible to 7. Perform division operation 25 \u00f7 5 = 5. The Estimated quotient is 7.<\/p>\n

Question 3.
\n121 \u00f7 12.75
\nAnswer:
\nEstimate 121 \u00f7 12.75. Use compatible numbers.
\nLook for compatible numbers.
\n121 \u00f7 12.75 is closes to 120 \u00f7 12 = 10.
\nSo, 121 \u00f7 12.75 is about 10.
\nThe Estimated quotient is 10.
\nExplanation:
\nCompatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 121 \u00f7 12.75 is closes to 120 \u00f7 12. The actual dividend 121 is compatible to 120. The actual divisor 12.75 is compatible to 12. Perform division operation 120 \u00f7 12 = 10. The Estimated quotient is 10.<\/p>\n

Question 4.
\n32.41 \u00f7 10.9
\nAnswer:
\nEstimate 32.41 \u00f7 10.9. Use rounding.
\nRound to the nearest ten: 32 rounds to 30; 10.9 rounds to 10.
\n32.41 \u00f7 10.9 is about 30 \u00f7 10 = 3.
\nExplanation:
\nRounding means replacing a number with an approximate value. In the above division method 32.41 \u00f7 10.9. Round the numbers to the nearest ten or hundreds. Here 32.41 is rounded to 30 and 10.9 is rounded to 10. Now perform division operation on 30 \u00f7 10 = 3. The estimated quotient is 3.<\/p>\n

Question 5.
\n82.4 \u00f7 3.7
\nAnswer:
\nEstimate 82.4 \u00f7 3.7. Use compatible numbers.
\nLook for compatible numbers.
\n82.4 \u00f7 3.7 is closes to 80 \u00f7 4 = 20.
\nSo, 82.4 \u00f7 3.7 is about 20.
\nThe Estimated quotient is 20.
\nExplanation:
\nCompatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 82.4 \u00f7 3.7 is closes to 80 \u00f7 4. The actual dividend 82.4 is compatible to 80. The actual divisor 3.7 is compatible to 4. Perform division operation 80 \u00f7 4 = 20. The Estimated quotient is 20.<\/p>\n

Question 6.
\n28.5 \u00f7 0.94
\nAnswer:
\nEstimate 28.5 \u00f7 0.94. Use compatible numbers.
\nLook for compatible numbers.
\n28.5 \u00f7 0.94 is closes to 30 \u00f7 1 = 30.
\nSo, 28.5 \u00f7 0.94 is about 30.
\nThe Estimated quotient is 30.
\nExplanation:
\nCompatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 28.5 \u00f7 0.94 is closes to 30 \u00f7 1. The actual dividend 28.5 is compatible to 30. The actual divisor 0.94 is compatible to 1. Perform division operation 30 \u00f7 1 = 30. The Estimated quotient is 30.<\/p>\n

Set C<\/strong>
\npages 237-240
\nFind 1.14 \u00f7 3.
\n\"Envision<\/p>\n

Remember<\/strong> to use estimation to check the placement of the decimal point in the quotient. Divide. Use models to help.<\/p>\n

Question 1.
\n6.58 \u00f7 7
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-60.2\"
\n6.58 \u00f7 7 = 0.94
\nExplanation:
\nIn the above image we can observe the division of 6.58 \u00f7 7 = 0.94. There are not enough ones to put 1 in each group, so regroup the 6 ones into 60 tenths. Divide 65 tenths into 7 equal groups. Each group gets 9 tenths. Seven groups of 0.9 = 6.3.
\nTrade the two extra tenth for 20 hundredths to get 28 hundredths. Divide the 28 hundredths into 7 equal groups. Each group gets 4 hundredths. Seven groups of 0.04 = 0.28.<\/p>\n

Question 2.
\n156 \u00f7 8
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-60.3\"
\n156 \u00f7 8 = 19.5
\nExplanation:
\nIn the above image we can observe the division of 156 \u00f7 8 = 19.5. There are enough ones to put 1 in each group, and extra ones is regrouped. Divide the 156 ones into 8 equal groups. Each group gets 19 ones. Eight groups of 19 = 152. Regroup of the 4 ones into 40 tenths.\u00a0 Divide the 40 tenths into 8 equal groups. Each group gets 5 tenths. Eight groups of 0.5 = 4.<\/p>\n

Question 3.
\n34.2 \u00f7 3
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-60.4\"
\n34.2 \u00f7 3 = 11.4
\nExplanation:
\nIn the above image we can observe the division of 34.2 \u00f7 3 = 11.4. There are enough ones to put 1 in each group, and extra ones is regrouped. Divide the 34 ones into 3 equal groups. Each group gets 11 ones. Three groups of 11 = 33. Regroup of the 1 one into 10 tenths.\u00a0 Divide the 12 tenths into 3 equal groups. Each group gets 4 tenths. Three groups of 0.4 = 1.2.<\/p>\n

Question 4.
\n5.84 \u00f7 4
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-60.5\"
\n5.84 \u00f7 4 = 1.46
\nExplanation:
\nIn the above image we can observe the division of 5.84 \u00f7 4 = 1.46. There are enough ones to put 1 in each group, and extra ones is regrouped. Divide the 5 ones into 4 equal groups. Each group gets 1 ones. Four groups of 1 = 4. Regroup of the 1 ones into 10 tenths. We can see that there are 18 tenths in 5.84. Divide the 18 tenths into 4 equal groups. Each group gets 4 tenths. Four groups of 0.4 = 1.6.
\nTrade the one extra tenth for 10 hundredths to get 24 hundredths. Divide the 24 hundredths into 4 equal groups. Each group gets 6 hundredths. Four groups of 0.06 = 0.24.<\/p>\n

Question 5.
\nMichelle pays $66.85 for a costume pattern and 8 yards of fabric. The costume pattern costs $4.85. How much does each yard of the fabric cost?
\nAnswer:<\/p>\n

Set D<\/strong>
\npages 241-244<\/p>\n

Find 94.5 \u00f7 15.
\nEstimate first
\n94.5 \u00f7 15 is close to 100 \u00f7 20 = 5, so start dividing with the ones place.
\n\"Envision
\nSo, 94.5 \u00f7 15 = 6.3<\/p>\n

Remember<\/strong> that you can check your calculation by multiplying the quotient by the divisor.<\/p>\n

Find each quotient.<\/p>\n

Question 1.
\n91.2 \u00f7 16
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-59.8(1)\"
\n91.2 \u00f7 16 = 5.7
\nExplanation:
\nIn the above image we can observe the division operation\u00a0 91.2 \u00f7 16 = 5.7. The nearest possible multiple value of 16 is 80(16 x 5). Subtract 80 from 91.2 so as to get the remainder 11.2. 16 cannot be a multiple of 11.2 and so we have kept a decimal in the quotient and now the possible multiple value of 16 near to 11.2 is 11.2 itself(16 x 0.7 = 11.2). Now the remainder is zero and the final quotient is 5.7.<\/p>\n

Question 2.
\n361.5 \u00f7 15
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-59.8(2)\"
\n361.5 \u00f7 15 = 24.1
\nExplanation:
\nIn the above image we can observe the division operation\u00a0 361.5 \u00f7 15 = 24.1. The nearest possible multiple value of 15 is 360(15 x 24). Subtract 360 from 361.5 so as to get the remainder 1.5. 15 cannot be a multiple of 1.5 and so we have kept a decimal in the quotient and now the possible multiple value of 15 near to 1.5 is 1.5 itself(15 x 0.1 = 1.5). Now the remainder is zero and the final quotient is 24.1.<\/p>\n

Question 3.
\n29.04 \u00f7 22
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-59.8(3)\"
\n29.04 \u00f7 22 = 1.32
\nExplanation:
\nIn the above image we can observe the division operation\u00a0 29.04 \u00f7 22 = 1.32. The nearest possible multiple value of 22 is 22(22 x 1). Subtract 22 from 29.04 so as to get the remainder 7.04. 22 cannot be a multiple of 7.04 and so we have kept a decimal in the quotient and now 22 has the least possible multiple value of 6.60(22 x 0.3) near to 7.04. After subtracting 6.6 from 7.04, we are now having 1.3 as quotient and 0.44as remainder. Now the possible multiple value of 22 near to 0.44 is 0.44 itself(22 x 0.02 = 0.44). Now the remainder is zero and the final quotient is 1.32.<\/p>\n

Question 4.
\n144 \u00f7 45
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-59.8(4)\"
\n144 \u00f7 45 = 3.2
\nExplanation:
\nIn the above image we can observe the division operation\u00a0 144 \u00f7 45= 3.2. The nearest possible multiple value of 45 is 135(45 x 3). Subtract 135 from 144 so as to get the remainder 9. 45 cannot be a multiple of 9 and so we have kept a decimal in the quotient and now the possible multiple value of 45 near to 9.0 is 9.0 itself(45 x 0.2 = 9.0). Now the remainder is zero and the final quotient is 3.2.<\/p>\n

Question 5.
\nA 12-ounce bottle of shampoo costs $4.20. A 16-ounce bottle costs $6.88. Which shampoo costs less per ounce? How do you know?
\nAnswer:
\nA 12-ounce bottle of shampoo costs $4.20.
\n$4.20 \u00f7 12 = $0.35.
\nA 16-ounce bottle costs $6.88.
\n$6.88 \u00f7 16 = $0.43
\n12- ounce bottle shampoo costs less per ounce is $0.35.
\nExplanation:
\nA 12-ounce bottle of shampoo costs $4.20. Divide $4.20 \u00f7 12 = $0.35. A 16-ounce bottle costs $6.88.\u00a0 Divide $6.88 \u00f7 16 = $0.43. Compare these 12- ounce and 16- ounce bottle of shampoos. The 12-ounce bottle shampoo costs less per ounce is $0.35.<\/p>\n

Set E<\/strong>
\npages 245-248<\/p>\n

Find 4.8 \u00f7 0.6.
\n\"Envision
\n48 tenths \u00f7 6 tenths
\n6 tenths \u00d7 ? = 48 tenths
\n? = 8
\nSo, 4.8 \u00f7 6 = 8<\/p>\n

Remember<\/strong> to use estimation Dates to check the quotient for reasonableness.<\/p>\n

Question 1.
\n6.4 \u00f7 3.2
\nAnswer:
\n6.4 \u00f7 3.2
\n3.2 x 2 = 6.4
\n6.4 \u00f7 3.2 = 2<\/strong>
\nThe quotient is 2.
\nExplanation:
\nMultiply 3.2 with 2 then the product is 6.4. Dividing 6.4 by 3.2 then the quotient is 2.<\/p>\n

Question 2.
\n6.4 \u00f7 0.32
\nAnswer:
\n0.32 x 20 = 6.4
\n6.4 \u00f7 0.32 = 20<\/strong>
\nThe quotient is 20.
\nExplanation:
\nMultiply 0.32 with 20 then the product is 6.4. Dividing 6.4 by 0.32 then the quotient is 20.<\/p>\n

Question 3.
\n9.6 \u00f7 0.8
\nAnswer:
\n12 x 8 = 96
\n12 x 0.8 = 9.6
\n9.6 \u00f7 0.8 = 12<\/strong>
\nThe quotient is 12.
\nExplanation:
\nMultiply 0.8 with 12 then the product is 9.6. Dividing 9.6 by 0.8 then the quotient is 12.<\/p>\n

Question 4.
\n0.96 \u00f7 0.08
\nAnswer:
\n12 x 8 = 96
\n12 x 0.08 = 0.96
\n0.96 \u00f7 0.08 = 12<\/strong>
\nThe quotient is 12.
\nExplanation:
\nMultiply 0.08 with 12 then the product is 0.96. Dividing 0.96 by 0.08 then the quotient is 12.<\/p>\n

Question 5.
\n41.8 \u00f7 2.2
\nAnswer:
\n19 x 2.2 = 41.8
\n41.8 \u00f7 2.2 = 19<\/strong>
\nThe quotient is 19.
\nExplanation:
\nMultiply 2.2 with 19 then the product is 41.8. Dividing 41.8 by 2.2 then the quotient is 19.<\/p>\n

Question 6.
\n4.18 \u00f7 0.22
\nAnswer:
\n0.22 x 19 = 4.18
\n4.18 \u00f7 0.22 = 19<\/strong>
\nThe quotient is 19.
\nExplanation:
\nMultiply 0.22 with 19 then the product is 4.18. Dividing 4.18 by 0.22 then the quotient is 19.<\/p>\n

Question 7.
\n81.4 \u00f7 7.4
\nAnswer:
\n11 x 7.4 = 81.4
\n81.4 \u00f7 7.4 = 11
\nThe quotient is 11<\/strong>.
\nExplanation:
\nMultiply 7.4 with 11 then the product is 81.4. Dividing 81.4 by 7.4 then the quotient is 11.<\/p>\n

Question 8.
\n814 \u00f7 74
\nAnswer:
\n814 \u00f7 74 = 11<\/strong>
\nThe quotient is 11.
\nExplanation:
\nBy Dividing 814 by 74 then the quotient is 11.<\/p>\n

Question 9.
\n9.6 \u00f7 0.03
\nAnswer:
\n9.6 \u00f7 0.03 = 320<\/strong>
\nThe quotient is 320.
\nExplanation:
\nBy Dividing 9.6 by 0.03 then the quotient is 320.<\/p>\n

Question 10.
\n9.6 \u00f7 0.3
\nAnswer:
\n9.6 \u00f7 0.3 = 32<\/strong>
\nThe quotient is 32.
\nExplanation:
\nBy Dividing 9.6 by 0.3 then the quotient is 32.<\/p>\n

Set F<\/strong>
\npages 249-252<\/p>\n

Think about these questions to help you reason abstractly and quantitatively.<\/p>\n

Thinking Habits<\/strong>
\n\u2022 What do the numbers and symbols in the problem mean?
\n\u2022 How are the numbers or quantities related?
\n\u2022 How can I represent a word problem using pictures, numbers, or equations?
\n\"Envision<\/p>\n

Zoey has a goal of saving $750 for a vacation. Her vacation will last 6 days. She wants to save the same amount each week for 12 weeks to reach her goal. How much should she save each week?
\nWhich quantities do you need to solve the problem?
\nThe savings goal is $750; Zoey will save for 12 weeks.<\/p>\n

Will Zoey need to save more than or less than $80 each week? Explain your reasoning.
\nLess than; 12 \u00d7 $80 = $960, but she only needs to save $750.
\nHow much should she save each week? Write an equation to represent the problem.
\n$62.50; $750 :12 = $62.50<\/p>\n

Remember<\/strong> to check the reasonableness of a solution by making sure your calculations are correct, and that you answered all of the questions that were asked.
\nlan uses 4 feet of ribbon to wrap each package. How many packages can he wrap with 5.6 yards of ribbon?<\/p>\n

Remember there are 3 feet in a yard.
\n\"Envision<\/p>\n

Question 1.
\nDescribe one way to solve the problem.
\nAnswer:<\/p>\n

Question 2.
\nWhat is the solution to the problem? Show your work.
\nAnswer:<\/p>\n

A bushel of apples weighs about 42 pounds. There are 4 pecks in a bushel. It takes 2 pounds of apples to make one pie. How many pies can you make with one peck of apples?<\/p>\n

Question 3.
\nHow are the numbers in the problem related?
\nAnswer:<\/p>\n

Question 4.
\nDescribe one way to solve the problem.
\nAnswer:<\/p>\n

Question 5.
\nSolve the problem. Show your work.
\nAnswer:<\/p>\n

Topic 6 Assessment Practice<\/h3>\n

Question 1.
\nMr. Dodd filled the gas tank on his lawn mower with 3.8 gallons of gas. He mowed his yard 10 times on the same tank of gas. He used the same amount of gas each time. How much gas did he use each time? Write an equation to show your work. Explain how the decimal point moves.
\nAnswer:<\/p>\n

Question 2.
\nKimberly scored a total of 35.08 points in four events for her gymnastic competition. If she scored the same number of points in each event, how many points did she score in each? Write an equation to show your work.
\nAnswer:
\n35.08 points \u00f7\u00a0 4 = 8.77 points.
\nShe scored 8.77 points in each event.
\nExplanation:
\nKimberly scored a total of 35.08 points in four events for her gymnastic competition. If she scored the same number of points in each event. Divide 35.08 by 4 then the quotient is 8.77. She scored 8.77 points in each event.<\/p>\n

Question 3.
\nChoose the correct quotient for each expression. Use number sense and estimation to help.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-70.1\"
\nExplanation:
\nPerform division operation on 21.6 \u00f7 1.8 = 12. The quotient is 12. Put a tick mark below the number 12.
\nPerform division operation on 10.23 \u00f7 0.55 = 18.6. The quotient is 18.6. Put a tick mark below the number 18.6.
\nPerform division operation on 78.75 \u00f7 3.5 = 22.5. The quotient is 22.5. Put a tick mark below the number 22.5.
\nPerform division operation on 29.67 \u00f7 4.6 = 18.6. The quotient is 18.6. Put a tick mark below the number 18.6.<\/p>\n

Question 4.
\nWhat is the value of the missing exponent in the equation?
\n\"Envision
\nA. 1
\nB. 2
\nC. 3
\nD. 4
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-80.2\"
\n80.5 \u00f7 102<\/sup> = 0.805
\nThe missing exponent in the equation is 2.<\/p>\n

Question 5.
\nThe chef at a restaurant bought 37 pounds of salad for $46.25. How much did she pay for each pound of salad?
\nA. 0.125
\nB. $1.25
\nC. $1.3
\nD. $12.50
\nAnswer:<\/p>\n

\"Envision-Math-Common-Core-Grade-5-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-80.2(1)\"
\n$46.25 \u00f7 37 = $1.25
\nShe pays $1.25 for each pound of salad.
\nExplanation:
\nThe chef at a restaurant bought 37 pounds of salad for $46.25. Divide $46.25 by 37 pounds then the quotient is $1.25. She pays $1.25 for each pound of salad.<\/p>\n

Question 6.
\nKathleen spent $231 on concert tickets for herself and 11 friends. Each ticket cost the same amount.
\nA. Estimate the cost of each ticket. Write an equation to show your work.
\nB. Find the exact cost of each ticket. Compare your answer to your estimate to check for reasonableness.
\nAnswer:
\nA. $231 \u00f7 12 = ?
\nEstimate $231 \u00f7 12 closes to 230 \u00f7 12 = $19.16.
\nThe estimated cost of each ticket is $19.16.
\nExplanation:
\nKathleen spent $231 on concert tickets for herself and 11 friends. Each ticket cost the same amount. Divide 230 by 12 then the quotient is $19.16. The estimated cost of each ticket is $19.16.
\nB. $231 \u00f7 12 = $19.25
\nThe actual cost of each ticket is $19.25.
\nExplanation:
\nThe estimated cost of each ticket is $19.16 and the actual cost of each ticket is $19.25.\u00a0 Both estimated answer and actual answer are reasonable.<\/p>\n

Question 7.
\nSelect all of the following equations that are true when 12.5 is used. Use number sense to help.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-80.6\"
\nExplanation:
\nIn the above image we can observe the equations that are true when 12.5 is used. Option 1 and option 3, option 5 is correct.
\n1. When 12.5 is divided by 10 then the quotient is 1.25. So option 1 is correct.
\n2. When 12.5 is divided by 1 then the quotient is 12.5. So option 2 is not correct.
\n3. When 12.5 is divided by 1 then the quotient is 12.5. So option 3 is correct.
\n4. When 12.5 is divided by 100 then the quotient is 0.125. So option 4 is not correct.
\n5. When 12.5 is divided by 100 then the quotient is 0.125. So option 5 is correct.<\/p>\n

Question 8.
\nWhich division problem does the model Tess made represent?
\n\"Envision
\nA. 1.35 \u00f7 3 = 0.45
\nB. 1.35 \u00f7 3 = 0.54
\nC. 1.62 \u00f7 3 = 0.45
\nD. 1.62 \u00f7 3 = 0.54
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-80.8\"
\nOption D 1.62 \u00f7 3 = 0.54 is correct.
\nExplanation:
\nIn the above image we can observe 5 tenths and 4 hundredths. By dividing 1.62 by 3 then the quotient is 0.54. The division problem answer option D represents the above image.<\/p>\n

Question 9.
\nIf 8 ounces of canned pumpkin has 82 calories, how many calories are in 1 ounce? Use your answer to find how many calories are in 6 ounces of pumpkin.
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-80.8(1)\"
\n10.25 calories are there in 1 ounce.
\n10.25 calories = 1 ounce
\n? calories\u00a0 \u00a0 = 6 ounces
\n10.25 calories x 6 ounces = 61.5 calories
\n61.5 calories are in 6 ounces of pumpkin.
\nExplanation:
\n8 ounces of canned pumpkin has 82 calories. Perform division operation on 82 \u00f7 8 = 10.25. There are 10.25 calories in 1 ounce. We have to find out the how many calories are there in 6 ounces. Perform multiplication operation on these two numbers 10.25 calories and 6 ounces then the product is 61.5 calories. There are 61.5 calories in 6 ounces of pumpkin.<\/p>\n

Question 10.
\nUse the equation 1.6 \u00f7 n = 0.016.
\nA. What value of n makes the equation true? Write your answer using an exponent.
\nB. Explain how you know your answer is correct.
\nAnswer:
\nA. 1.6 \u00f7 n = 0.016.
\n1.6 \u00f7 0.01 = 0.016.
\n1.6 \u00f7 10-2<\/sup> = 0.016.
\nThe value n = 0.01 makes the equation true. The exponent form of 0.01 is 10-2<\/sup> .
\nB. We can check the answer is correct or not by performing division operation on 0.016 \u00f7 1.6 = 0.01.<\/p>\n

Question 11.
\nEileen bought 8 roses for $45.50. Which is the best way to estimate the cost of one rose?
\nA. $45 \u00f7 5 = $9.00
\nB. $48 \u00f7 8 = $6.00
\nC. $45 \u00f7 10 = $0.45
\nD. $40 \u00f7 8 = $0.50
\nAnswer:
\nOption B $48 \u00f7 8 = $6.00<\/strong> is the best way to estimate the cost of one rose.<\/p>\n

Estimate $45.50\u00f7 8. Use compatible numbers.
\nLook for compatible numbers.
\n$45.50\u00f7 8 is closes to $48 \u00f7 8 = $6.
\nThe Estimated cost of one rose is $6.
\nExplanation:
\nCompatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. Eileen bought 8 roses for $45.50. In the above division problem $45.50\u00f7 8 is closes to 48 \u00f7 8. The actual dividend $45.50 is compatible to 48. Perform division operation $48 \u00f7 8 = 6. The Estimated cost of one rose is $6.<\/p>\n

Question 12.
\nToby’s faucet dripped a total of 1.92 liters of water in 24 hours. The faucet dripped the same amount each hour.
\nA. Estimate how many liters his faucet dripped each hour. Write an equation to model your work.
\nB. Find the exact amount of water that dripped each hour.
\nC. Compare your estimate to your answer. Is your answer reasonable? Explain.
\nAnswer:
\nA. 1.92 liters \u00f7 24 = ?
\nEstimate 1.92 liters \u00f7 24 closes to 2 liters \u00f7 24 = 0.083 liters.
\nThe estimated amount of water dripped each hour is 0.083 liters.
\nExplanation:
\nToby’s faucet dripped a total of 1.92 liters of water in 24 hours. Divide 2liters by 24 then the result is 0.083 liters. The estimated amount of water dripped each hour is 0.083 liters.
\nB. 1.92 liters \u00f7 24 = 0.08 liters.
\nThe exact amount of water that dripped each hour is 0.08 liters.
\nExplanation:
\nPerform division operation on 1.92 liters by 24 hours. The quotient is 0.08 liters. The exact amount of water that dripped each hour is 0.08 liters.
\nc. The estimated amount of water dripped each hour is 0.083 liters.
\nThe exact amount of water that dripped each hour is 0.08 liters. The answer is reasonable.<\/p>\n

Topic 6 Assessment Practice<\/h3>\n

Question 13.
\nChoose the correct quotient for each expression.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-85.1\"
\nExplanation:
\nPerform division operation on 0.78 \u00f7 10 = 0.078. The quotient is 0.078. Put a tick mark below the number 0.078.
\nPerform division operation on 7,080 \u00f7 103<\/sup> = 7.08. The quotient is 7.08. Put a tick mark below the number 7.08.
\nPerform division operation on 70.8 \u00f7 102<\/sup> = 0.708. The quotient is 0.708. Put a tick mark below the number 0.708.
\nPerform division operation on 780 \u00f7 103<\/sup> = 0.78. The quotient is 0.78. Put a tick mark below the number 0.78.<\/p>\n

Question 14.
\nDiego is making a large mural. He draws a hexagon with a perimeter of 10.5 meters. Each side of the hexagon is the same length.
\n\"Envision
\nA. How many meters long is each side of Diego’s hexagon? Write an equation to model your work.
\nB. The total cost of the supplies to paint the mural is $38.70. Diego and 9 friends divide the total cost equally. How much does each person pay?
\nAnswer:<\/p>\n

Question 15.
\nSelect all of the following equations that are true when 40.3 is used. Use number sense to help.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-86.1\"
\nExplanation:
\nIn the above image we can observe the equations in option 2 and option 3 are true when 40.3 is used.
\nPerform division operation on 40.3 \u00f7 102 <\/sup>= 0.403. The quotient is 0.403. So option 2 is correct.
\nPerform division operation on 40.3 \u00f7 100 <\/sup>= 40.3. The quotient is 40.3. So option 3 is correct.<\/p>\n

Question 16.
\nLou’s Diner spent $12.80 on 8 pounds of potatoes. What was the cost of one pound of potatoes? What would be the total cost if the cost per pound remained the same and the diner bought 7 pounds? Show your work.
\nAnswer:
\n$12.80 \u00f7 8 pounds = $1.6
\nThe cost of one pound of potatoes is $1.6.
\n? \u00f7 7 pounds = $1.6
\n$1.6 x 7 pounds = $11.2
\nThe total cost is $11.2. If the cost per pound remains same and the dinner bought 7 pounds.
\nExplanation:
\nLou’s Diner spent $12.80 on 8 pounds of potatoes. Divide $12.80 \u00f7 8 pounds = $1.6. The cost of one pound of potatoes is $1.6. If the cost per pound remains same and the dinner bought 7 pounds. Multiply $1.6 x 7 pounds = $11.2. The total cost is $11.2.<\/p>\n

Question 17.
\nHow many quarters are there in $30? Solve the equation 30 \u00f7 0.25 to help you.
\nA. 12 quarters
\nB. 20 quarters
\nC. 120 quarters
\nD. 200 quarters
\nAnswer:
\n30 \u00f7 0.25 = 120
\nThere are 120 quarters in $30.
\nOption C is correct.
\nExplanation:
\nPerform division operation on 30 \u00f7 0.25 = 120 . Here the dividend is 30 and the divisor is 0.25. By dividing the dividend with divisor then the quotient is 120. There are 120 quarters in $30. So option C is correct.<\/p>\n

Question 18.
\nWhen solving 6.1 \u00f7 102<\/sup>, how is the decimal point moved?
\nA. 1 place to the right
\nB. 1 place to the left
\nC. 2 places to the right
\nD. 2 places to the left
\nAnswer:
\n6.1 \u00f7 102 <\/sup>\u00a0= 0.061
\nOption D<\/strong> is correct .
\nExplanation:
\nPerform division operation on 6.1 \u00f7 102 <\/sup>\u00a0= 0.061 . Here the divisor is 102<\/sup>\u00a0 which is 100. So the decimal point is moved two places to the left. The quotient is 0.061. So option D is correct.<\/p>\n

Question 19.
\nA group of 5 friends bought a bag of grapes to share equally. If the bag of grapes weighs 11.25 pounds, how much is each person’s share? How many friends could share the grapes if each person’s share was 1.25 pounds? Write an equation to model your work.
\nAnswer:
\n11.25 pounds\u00a0 \u00f7 5 = 2.25 pounds.
\nEach person share is 2.25 pounds.
\n11.25 pounds \u00f7 ? = 1.25 pounds.
\n11.25 pounds \u00f7 9 = 1.25 pounds.
\n9 friends can share the grapes if each person’s share was 1.25 pounds.
\nExplanation:
\nA group of 5 friends bought a bag of grapes to share equally. The bag of grapes weighs 11.25 pounds. Perform division operation on 11.25 pounds\u00a0 \u00f7 5 = 2.25 pounds. Each person share is 2.25 pounds.
\nDivide 11.25 pounds \u00f7 1.25 pounds = 9. Nine friends can share the grapes if each person’s share was 1.25 pounds.<\/p>\n

Question 20.
\nWhen dividing 560.9 by 100, how should the decimal point be moved?
\nAnswer:
\n560.9 \u00f7 100 = 5.609
\nExplanation:
\nDividing by 100, or 102<\/sup>, means moving the decimal point two places to the left. Move the dividend decimal point 560.9 two places to the left then the result is 5.609. The quotient is 5.609.<\/p>\n

Question 21.
\nJune says that there should be a decimal point in the quotient below after the 4. Is she correct? Use number sense to explain your answer. 43.94 \u00f7 5.2 = 845
\nAnswer:
\n43.94 \u00f7 5.2 = 8.45
\nShe is not correct. The decimal should be placed after 8.
\nExplanation:
\nJune says that there should be a decimal point in the quotient after the 4. She is not correct because we have to place the decimal point after 8.<\/p>\n

Question 22.
\nThree coworkers decided to buy fruit to share at lunchtime. Antonio spent $1.47 on bananas. Laura spent $2.88 on apples. Suzanne spent $2.85 on oranges.
\nA. Complete the bar diagram to find out how much they spent in all on fruit.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-87.2\"
\nThey spent $7.2 in all on fruit.
\nExplanation:
\nThree coworkers decided to buy fruit to share at lunchtime. Antonio spent $1.47 on bananas. Laura spent $2.88 on apples. Suzanne spent $2.85 on oranges. Add all fruit costs. Add $1.47 with $2.88 and $2.85 then the sum is $7.2. They spent $7.2 in all on fruit.<\/p>\n

B. They evenly divided the cost of the 3 types of fruit. How much did each person pay? Complete the bar diagram to help you.
\n\"Envision
\nAnswer:
\n\"Envision-Math-Common-Core-Grade-5-Answers-Topic-6-Use-Model-Strategies-to-Divide-Decimals-87.3\"
\nEach person has to pay $2.4 for fruits.
\nExplanation:
\nThe three coworkers evenly divided the cost of the 3 types of fruit. The total cost of three fruits is $7.2. Divide $7.2 by 3 then the quotient is $2.4. Each person has to pay $2.4 for fruits.<\/p>\n

C. If Laura bought 2.1 pounds of apples, is the price per pound of apples greater than or less than $1? How can you tell?
\nAnswer:<\/p>\n

Topic 6 Performance Task<\/h3>\n

Cooking Competition<\/strong>
\nLydia is organizing a cooking competition at her school. She ordered some basic supplies to share among the teams that are competing. The teams will be bringing other ingredients as well.<\/p>\n

Use the list at the right to answer the questions.<\/p>\n

Question 1.
\nIf 10 of the teams divide the olive oil equally, how much will each team receive? Write an equation to model your work.
\n\"Envision
\nAnswer:
\n5.4 liters \u00f7 10 = 0.54 liters.
\nEach team receives 0.54 liters.
\nExplanation:
\n10 of the teams divide the olive oil equally. Here we have total 5.4 liters of olive oil. Perform division operation on 5.4 liters \u00f7 10 = 0.54 liters. Each team receives 0.54 liters.<\/p>\n

Question 2.
\nEight teams agree to share the flour equally.
\nPart A<\/strong>
\nAbout how many grams of flour will each team get? Use compatible numbers to estimate. Write an equation to show how you estimated.
\nAnswer:
\n738.4 grams \u00f7 8\u00a0 = ?.
\nEstimate 738.4 grams \u00f7 8. Use compatible numbers.
\nLook for compatible numbers.
\n738.4 \u00f7 8 is closes to 738 \u00f7 8 = 92.25 grams.
\nThe Estimated quotient is 92.25.
\nEach team get 92.25 grams of flour.
\nExplanation:
\nCompatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 738.4 grams \u00f7 8 is closes to 738 \u00f7 8. The actual dividend738.4 is compatible to 738.\u00a0 Perform division operation 738 \u00f7 8 = 92.25. The Estimated quotient is 92.25. Each team get 92.25 grams of flour.
\nPart B<\/strong>
\nFind the actual amount of flour each team will receive. Show your work.
\nAnswer:
\n738.4 grams \u00f7 8\u00a0 = 92.3 grams.
\nEach team will receive 92.3 grams of flour.
\nExplanation:
\nPerform division operation on 738.4 grams \u00f7 8\u00a0 = 92.3 grams. Each team will receive the actual amount of flour is 92.3 grams.<\/p>\n

Question 3.
\nSeveral teams agree to share the salt equally. Each team will be given 7.3 grams of salt. How many teams agree to share the salt? Write a division equation to model the problem. Then write an equivalent equation using whole numbers.
\nAnswer:
\n87.6 grams \u00f7 ? = 7.3 grams.
\n87.6 grams \u00f7 12 = 7.3 grams.
\n12 teams agree to share the salt.
\nExplanation:
\nSeveral teams agree to share the salt equally. Each team will be given 7.3 grams of salt. The division equation is 87.6 grams \u00f7 ? = 7.3 grams. Divide 87.6 with 7.3 then the answer is 12. 12 teams agree to share the salt.<\/p>\n

Question 4.
\nMalcolm calculated how many liters of milk each team would get if 6 teams shared the milk equally. His work is shown at the right, but he forgot to place the decimal point in the quotient. Where should he place the decimal point? Explain.
\nAnswer:<\/p>\n

\"Envision
\n8.25 liters \u00f7 6 = 1.375 liters.
\nMalcolm has to place the decimal point before 3 and after 1.
\nEach team get 1.375 liters of milk.
\nExplanation:
\nMalcolm calculated how many liters of milk each team would get if 6 teams shared the milk equally. His work is shown above, but he forgot to place the decimal point in the quotient. He has to place the decimal point before 3 and after 1. Each team get 1.375 liters of milk.<\/p>\n

Question 5.
\nLydia decides to provide cheddar cheese for the competition. She buys 4.2 kilograms for $39.90.
\nPart A<\/strong>
\nShe estimates the cost of 1 kilogram of cheese to be $1. Is her estimate reasonable? Explain.
\nAnswer:
\n4.2 kilograms \u00f7 $39.90 = ?
\nEstimate 4.2 \u00f7 $40 = $0.105
\nThe cost of 1 kilogram of cheese to be $0.105. Her Estimation is not reasonable.
\nExplanation:
\nLydia decides to provide cheddar cheese for the competition. She buys 4.2 kilograms for $39.90. Perform division operation on 4.2 \u00f7 $40 = $0.105. The cost of 1 kilogram of cheese to be $0.105. Her Estimation is not reasonable.
\nPart B<\/strong>
\nTo find the actual cost of 1 kilogram of cheese, Lydia needs to divide $39.90 by 4.2. How can she change the division problem to an equivalent problem using whole numbers? Write and solve the equivalent problem..
\nPart C<\/strong>
\nIf 7 teams share the cheese equally, how much cheese will each team get?
\nAnswer:
\n4.2 kilograms \u00f7\u00a0 7 = 0.6 kilograms.
\nEach team get 0.6 kilograms of cheese equally.
\nExplanation:
\nThe cheese we have is 4.2 kilograms. Seven teams takes the cheese equally. perform division operation on 4.2 kilograms \u00f7\u00a0 7 = 0.6 kilograms. Each team get 0.6 kilograms of cheese equally.<\/p>\n","protected":false},"excerpt":{"rendered":"

Go through the\u00a0enVision Math Common Core Grade 5 Answer Key\u00a0Topic 6 Use Models and Strategies to Divide Decimals\u00a0regularly and improve your accuracy in solving questions. enVision Math Common Core 5th Grade Answers Key Topic 6 Use Model Strategies to Divide Decimals enVision STEM Project: States of Water Do Research Use the Internet or other sources …<\/p>\n","protected":false},"author":1,"featured_media":25610,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/09\/enVision-Math-Common-Core-Grade-5-Answer-Key-Topic-6-Use-Model-Strategies-to-Divide-Decimals.png","_links":{"self":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/11351"}],"collection":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/comments?post=11351"}],"version-history":[{"count":2,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/11351\/revisions"}],"predecessor-version":[{"id":27348,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/11351\/revisions\/27348"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/media\/25610"}],"wp:attachment":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/media?parent=11351"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/categories?post=11351"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/tags?post=11351"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}