{"id":10410,"date":"2024-01-03T12:01:02","date_gmt":"2024-01-03T06:31:02","guid":{"rendered":"https:\/\/envisionmathanswerkey.com\/?p=10410"},"modified":"2024-01-04T10:07:04","modified_gmt":"2024-01-04T04:37:04","slug":"envision-math-common-core-grade-5-answer-key-topic-4","status":"publish","type":"post","link":"https:\/\/envisionmathanswerkey.com\/envision-math-common-core-grade-5-answer-key-topic-4\/","title":{"rendered":"enVision Math Common Core Grade 5 Answer Key Topic 4 Use Models and Strategies to Multiply Decimals"},"content":{"rendered":"

Go through the\u00a0enVision Math Common Core Grade 5 Answer Key<\/a>\u00a0Topic 4 Use Models and Strategies to Multiply Decimals<\/strong>\u00a0regularly and improve your accuracy in solving questions.<\/p>\n

enVision Math Common Core 5th Grade Answers Key Topic 4 Use Models and Strategies to Multiply Decimals<\/h2>\n

Essential Question:<\/strong> What are some common procedures for estimating and finding products involving decimals?<\/p>\n

\"Envision
\nenVision STEM Project: Solar Energy<\/strong>
\nDo Research<\/strong> Use the Internet or other sources to learn about solar energy. Find at least five ways that we use the Sun’s energy today.<\/p>\n

Answer:
\nTo dry your clothes.
\nTo grow your food.
\nTo heat your water.
\nTo power your car.
\nTo generate your electricity.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe sun has gone to a lot of trouble to send us its energy.
\nwe can use solar energy in many ways.
\nthey are:
\nto dry your clothes.
\nto grow your food.
\nto heat your water.
\nto power your car.
\nto generate your electricity.<\/p>\n

Journal: Write a Report<\/strong> Include what you found. Also in your report:
\n\u2022 Describe at least one way that you could use solar energy. Could it save you money?
\n\u2022 Estimate how much your family pays for energy costs such as lights, gasoline, heating, and cooling.
\n\u2022 Make up and solve problems by multiplying whole numbers and 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 exponent
\n\u2022 hundredths
\n\u2022 overestimate
\n\u2022 partial products
\n\u2022 power
\n\u2022 round
\n\u2022 tenths
\n\u2022 thousandths
\n\u2022 underestimate<\/p>\n

\"Use<\/p>\n

Question 1.
\nOne way to estimate a number is to ____ the number.<\/p>\n

Answer:
\nOne way to estimate a number is to round the number.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\none way to estimate a number is to round the number.
\nfor example:
\n2.456 round to tenths.
\n2.556.<\/p>\n

Question 2.
\nUsing 50 for the number of weeks in a year is a(n) _____.<\/p>\n

Answer:
\nUsing 50 for the number of weeks in a year is a(n) is exponents.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nusing 50 for the number of weeks in a year is a(n) is exponents.
\nfor example:
\na(n) = 50.
\na = 5.
\n50\/5 = 10.<\/p>\n

Question 3.
\nIn the number 3.072, the digit 7 is in the ___ place and the digit 2 is in the ____ place.<\/p>\n

Answer:
\nIn the number 3.072, the digit 7 is in the hundredths place and the digit 2 is in the thousandths place.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nIn the number 3.072, the digit 7 is in the hundredths place and the digit 2 is in the thousandths place.
\nfor example:
\n3.072.
\n7 is in the hundredths place.
\n2 is in the thousands place.<\/p>\n

Question 4.
\n10,000 is a(n) ____ of 10 because 10 \u00d7 10 \u00d7 10 \u00d7 10 = 10,000.<\/p>\n

Answer:
\n10,000 is a(n) power of 10 because 10 x 10 x 10 x 10 = 10,000.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nfor example:
\n10 x 10 x 10 x 10.
\n100 x 100 = 10,000.<\/p>\n

Whole Number Multiplication Find each product.<\/p>\n

\"Use<\/p>\n

Question 5.
\n64 \u00d7 100<\/p>\n

Answer:
\nThe product is 6400.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 64 and 100.
\nmultiply the two numbers.
\n64 x 100 = 6400.
\nso the product is 6400.<\/p>\n

Question 6.
\n7,823 \u00d7 103<\/sup><\/p>\n

Answer:
\nThe product is 7823000.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 7823 and 1000.
\nmultiply the two numbers.
\n7823 x 1000 = 7823000.
\nso the product is 7823000.<\/p>\n

Question 7.
\n10 \u00d7 1,405<\/p>\n

Answer:
\nThe product is 14050.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 10 and 1405.
\nmultiply the two numbers.
\n10 x 1405 = 14050.
\nso the product is 14050.<\/p>\n

Question 8.
\n53 \u00d7 413<\/p>\n

Answer:
\nThe product is 21889.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 53 and 413.
\nmultiply the two numbers.
\n53 x 413 = 21889.
\nso the product is 21889.<\/p>\n

Question 9.
\n906 \u00d7 57<\/p>\n

Answer:
\nThe product is 51,642.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 906 and 57.
\nmultiply the two numbers.
\n906 x 57 = 51,642.
\nso the product is 51,642.<\/p>\n

\"Use<\/p>\n

Question 10.
\n1,037 \u00d7 80<\/p>\n

Answer:
\nThe product is 82,960.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 1037 and 80.
\nmultiply the two numbers.
\n1037 x 80 = 82,960.
\nso the product is 82,960.<\/p>\n

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

Round each number to the nearest tenth.<\/p>\n

Question 11.
\n842.121<\/p>\n

Answer:
\nThe number to the nearest tenth = 842.10.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe number is 842.121.
\nto round a number to the nearest tenth look at the number of ones.
\nif this is 5 or more round up.
\nif it is 4 or less round down.
\n842.10.
\nso the number to the nearest tenth = 842.10.<\/p>\n

Question 12.
\n10,386.145<\/p>\n

Answer:
\nThe number to the nearest tenth = 10386.10.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe number is 10,386.145.
\nto round a number to the nearest tenth look at the number of ones.
\nif this is 5 or more round up.
\nif it is 4 or less round down.
\n10386.10.
\nso the number to the nearest tenth = 10386.10.<\/p>\n

Question 13.
\n585.055<\/p>\n

Answer:
\nThe number to the nearest tenth = 585.155.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe number is 585.055.
\nto round a number to the nearest tenth look at the number of ones.
\nif this is 5 or more round up.
\nif it is 4 or less round down.
\n585.055.
\nso the number to the nearest tenth = 585.155.<\/p>\n

Properties of Multiplication<\/strong>
\nUse the Commutative and Associative Properties of Multiplication to complete each multiplication.<\/p>\n

\"Use<\/p>\n

Question 14.
\n96 \u00d7 42 = 4,032 so 42 \u00d7 96 = ___<\/p>\n

Answer:
\n42 x 96 = 4032.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 96 and 42.
\nmultiply the two numbers.
\n96 x 42 = 4032.
\n42 x 96 = 4032.<\/p>\n

Question 15.
\n4 (58 \u00d7 25) = 4 \u00d7 (25 \u00d7 ___) = (___ \u00d7 ___) \u00d7 58 = ___<\/p>\n

Answer:
\n4(58 x 25) = 4 x (25 x 58) = (25 x 4) x 58 = 5800.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 58, 4, and 25.
\nmultiply the two numbers.
\n4 x 25 x 58.
\n25 x 4 x 8 = 5800.<\/p>\n

Question 16.
\n(293 \u00d7 50) \u00d7 20 = 293 \u00d7 (50 \u00d7 ___) = ___<\/p>\n

Answer:
\n293 x 50 x 20 = 293 x 50 x 20 = 2,93,000.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 293, 50, and 20.
\nmultiply the two numbers.
\n293 x 50 x 20.
\n50 x 293 x 20 = 2,93,000.<\/p>\n

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

PROJECT 4A<\/strong><\/p>\n

How can you set up an exercise plan?
\nProject: Plan an exercise Program
\n\"Envision<\/p>\n

PROJECT 4B<\/strong>
\nHow much does it cost to dress a team?
\nProject: Budget a Team
\n\"Envision<\/p>\n

PROJECT 4C<\/strong>
\nHow far can a rocket go in 100 seconds?
\nProject: Make a Poster
\n\"Envision<\/p>\n

Answer:
\nThe rocket can go in 100 sec = 790 km.<\/p>\n

Explanation:
\nThe above-given question,
\ngiven that,
\nthe rocket can go in 100 sec is:
\n1 minute = 60 sec.
\n1 sec = 7.9 km.
\n100sec = 7.9 x 100.
\n790 km.<\/p>\n

PROJECT 4D<\/strong>
\nHow much extra do you have to pay?
\nProject: Make a Data Display
\n\"Envision<\/p>\n

Lesson 4.1 Multiply Decimals by Powers of 10<\/h3>\n

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

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

Javier is helping his parents put up posters in their movie theater. Each poster has a thickness of 0.012 inch. How thick is a stack of 10 posters? 100 posters? 1,000 posters? Solve this problem any way you choose.<\/p>\n

Answer:
\nThe thick is a stack of 10 posters = 0.12.
\nthe thick is a stack of 100 posters = 1.2.
\nthe thick is a stack of 1000 posters = 12.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJavier is helping his parents put up posters in their movie theater.
\nEach poster has a thickness of 0.012.
\n0.012 x 10 = 0.12.
\n0.012 x 100 = 1.2.
\n0.012 x 1000 = 12.<\/p>\n

You can use the structure of our number system and mental math to help you.
\n\"Envision<\/p>\n

Look Back!<\/strong> Use Structure<\/strong> How is your answer for 1,000 posters similar to 0.012? How is it different?<\/p>\n

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

Essential Question<\/strong>
\nWhat Patterns Can Help You Multiply Decimals by Powers of 10?<\/p>\n

A.<\/strong>
\nYou can use place value and what you know about whole numbers to multiply decimals by powers of 10. What patterns can you find?<\/p>\n

We already know what happens when a whole number is multiplied by powers of 10.
\n\"Envision
\n\"Envision<\/p>\n

B.<\/strong>
\nIn a place-value chart, the same pattern appears when a decimal is multiplied by powers of 10.
\n\"Envision
\nA digit in one place is worth 10 times more when moved to the place on its left. Every time a number is multiplied by 10, the digits of the number shift to the left.<\/p>\n

C.<\/strong>
\nHolding the numbers still, another pattern appears.
\n3.63 \u00d7 1 = 3.63
\n3.63 \u00d7 101<\/sup> = 36.3
\n3.63 \u00d7 102<\/sup> = 363.0
\n3.63 \u00d7 103<\/sup> = 3630.0
\nIt looks like the decimal point moves to the right each time.
\n\"Envision<\/p>\n

Convince Me!<\/strong> Use Structure Complete the chart. What patterns can you use to place the decimal point?
\n\"Envision<\/p>\n

Answer:
\n1.275 x 10 = 12.75, 1.275 x 100 = 127.5, 1.275 x 1000 = 1275.
\n26.014 x 10 = 260.14, 26.014 x 100 = 2601.4, 26.014x 1000 = 26014.
\n0.4 x 10 = 4, 0.4 x 100 = 40, 0.4 x 1000 = 400.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 1.275, 26.014, and 0.4.
\nmultiply the numbers by 10, 100, and 1000.
\n1.275 x 10 = 12.75, 1.275 x 100 = 127.5, 1.275 x 1000 = 1275.
\n26.014 x 10 = 260.14, 26.014 x 100 = 2601.4, 26.014x 1000 = 26014.
\n0.4 x 10 = 4, 0.4 x 100 = 40, 0.4 x 1000 = 400.
\n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-4-<\/p>\n

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

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

Question 1.
\nWhen multiplying by a power of 10, like 4.58 \u00d7 103<\/sup>, how do you know you are moving the decimal in the correct direction?<\/p>\n

Answer:
\nThe number is 4580.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n4.58 \u00d7 103.
\n<\/sup>4.58 x 10 x 10 x 10.
\n4.58 x 1000 = 4580.
\nso the number is 4580.<\/p>\n

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

In 2-5, find each product.<\/p>\n

Question 2.
\n0.009 \u00d7 10<\/p>\n

Answer:
\nThe product is 0.09.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.009\u00a0 and 10.
\nmultiply the numbers.
\n0.009 x 10 = 0.09.
\nso the product is 0.09.<\/p>\n

Question 3.
\n3.1 \u00d7 103<\/sup><\/p>\n

Answer:
\nThe product is 3100.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 3.1 and 1000.
\nmultiply the numbers.
\n3.1 x 1000 = 3100.
\nso the product is 3100.<\/p>\n

Question 4.
\n0.062 \u00d7 102<\/sup><\/p>\n

Answer:
\nThe product is 6.2.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.062\u00a0 and 100.
\nmultiply the numbers.
\n0.062 x 100 = 6.2.
\nso the product is 6.2.<\/p>\n

Question 5.
\n1.24 \u00d7 104<\/sup><\/p>\n

Answer:
\nThe product is 1240.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 1.24\u00a0 and 10000.
\nmultiply the numbers.
\n1.24 x 10000 = 1240.
\nso the product is 1240.<\/p>\n

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

Leveled Practice<\/strong> in 6 and 7, find each product.<\/p>\n

Place-value patterns can help you solve these problems.
\n\"Envision<\/p>\n

Question 6.
\n42.3 \u00d71 = ___
\n42.3 \u00d7 10 = ___
\n42.3 \u00d7 102<\/sup> = ___<\/p>\n

Answer:
\n42.3 x 1 = 42.3.
\n42.3 x 10 = 423.
\n42.3 x 100 = 4230.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 42.3, 42.2 x 10, and 42.3 x 100.
\n42.3 x 1 = 42.3.
\n42.3 x 10 = 423.
\n42.3 x 100 = 4230.<\/p>\n

Question 7.
\n____ = 0.086 \u00d7 101<\/sup>
\n___ = 0.086 \u00d7 100
\n____ = 0.086 \u00d7 1,000<\/p>\n

Answer:
\n0.086 x 10 = 0.86.
\n0.086 x 100 = 8.6.
\n0.086 x 1000 = 86.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.086 x 10, 0.086 x 100, and 0.086 x 1000.
\n0.086 x 10 = 0.86.
\n0.086 x 100 = 8.6.
\n0.086 x 1000 = 86.<\/p>\n

In 8-15, find each product.<\/p>\n

Question 8.
\n63.7 \u00d7 10<\/p>\n

Answer:
\nThe product is 637.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 63.7\u00a0 and 10.
\nmultiply the numbers.
\n63.7 x 10 = 637.
\nso the product is 637.<\/p>\n

Question 9.
\n563.7 \u00d7 102<\/sup><\/p>\n

Answer:
\nThe product is 56370.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 563.7\u00a0 and 100.
\nmultiply the numbers.
\n563.7 x 100 = 56370.
\nso the product is 56370.<\/p>\n

Question 10.
\n0.365 \u00d7 104<\/sup><\/p>\n

Answer:
\nThe product is 3650.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.365\u00a0 and 10000.
\nmultiply the numbers.
\n0.365 x 10000 = 3650.
\nso the product is 3650.<\/p>\n

Question 11.
\n5.02 \u00d7 100<\/p>\n

Answer:
\nThe product is 502.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 5.02\u00a0 and 100.
\nmultiply the numbers.
\n5.02 x 100 = 502.
\nso the product is 502.<\/p>\n

Question 12.
\n94.6 \u00d7 103<\/sup><\/p>\n

Answer:
\nThe product is 94600.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 94.6\u00a0 and 1000.
\nmultiply the numbers.
\n94.6 x 1000 = 94600.
\nso the product is 94600.<\/p>\n

Question 13.
\n0.9463 \u00d7 102<\/sup><\/p>\n

Answer:
\nThe product is 94.63.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.9463\u00a0 and 100.
\nmultiply the numbers.
\n0.9463 x 100 = 94.63.
\nso the product is 94.63.<\/p>\n

Question 14.
\n0.678 \u00d7 100<\/p>\n

Answer:
\nThe product is 67.8.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.678\u00a0 and 100.
\nmultiply the numbers.
\n0.678 x 100 = 67.8.
\nso the product is 67.8.<\/p>\n

Question 15.
\n681.7 \u00d7 104<\/sup><\/p>\n

Answer:
\nThe product is 6817000.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 681.7 and 10000.
\nmultiply the numbers.
\n681.7 x 10000 = 6817000.
\nso the product is 6817000.<\/p>\n

In 16-18, find the missing exponent.<\/p>\n

Question 16.
\n0.629 \u00d7 \"Envision = 62.9<\/p>\n

Answer:
\nThe missing exponent is 2.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n0.629 x 10 x 10.
\n0.629 x 100 = 62.9.
\n0.629<\/p>\n

Question 17.
\n\"Envision \u00d7 0.056 = 560<\/p>\n

Answer:
\nThe missing exponent is 4.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n10 x 10 x 10 x 10 x 0.056.
\n100 x 100 x 0.056.
\n10000 x 0.056.
\n560.<\/p>\n

Question 18.
\n1.23 = \"Envision \u00d7 0.123<\/p>\n

Answer:
\nThe missing exponent is 0.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n1.23 x 10.
\n1.23.<\/p>\n

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

In 19-21, use the table to find the answers.<\/p>\n

Question 19.
\nMonroe uses a microscope to observe specimens in science class. The microscope enlarges objects to 100 times their actual size. Find the size of each specimen as seen in the microscope.<\/p>\n

Answer:
\nThe size of each specimen as seen in the microscope = 0.8, 11, 0.25, and 0.4.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nMonroe uses a microscope to observe specimens in science class.
\nThe microscope enlarges objects to 100 times their actual size.
\n0.008 x 100 = 0.8.
\n0.011 x 100 = 11.
\n0.0025 x 100 = 0.25.
\n0.004 x 100 = 0.4.<\/p>\n

\"Envision
\n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-4-<\/p>\n

Question 20.
\nMonroe’s teacher wants each student to draw a sketch of the longest specimen. Which specimen is the longest?<\/p>\n

Answer:
\nSpecimen B is the longest.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nMonroe’s teacher wants each student to draw a sketch of the longest specimen.
\n0.008 x 100 = 0.8.
\n0.011 x 100 = 11.
\n0.0025 x 100 = 0.25.
\n0.004 x 100 = 0.4.
\nso specimen B is the longest.<\/p>\n

Question 21.
\nSeen through the microscope, a specimen is 0.75 cm long. What is its actual length?<\/p>\n

Answer:
\nThe actual length = 75 cm.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\na specimen is 0.75 cm long.
\n0.75 x 100 = 75.
\nso the actual length of the specimen is 75 cm.<\/p>\n

Question 22.
\nJon’s binoculars enlarge objects to 10 times their actual size. If the length of an ant is 0.43 inch, what is the length as seen up close through his binoculars?<\/p>\n

Answer:
\nThe length as seen up close through his binoculars = 4.3 inches.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJon’s binoculars enlarge objects to 10 times their actual size.
\nIf the length of an ant is 0.43 inches.
\n0.43 x 10 = 4.3 inches.
\nso the length as seen up close through his binoculars = 4.3 inches.<\/p>\n

Question 23.
\nHigher Order Thinking<\/strong> Jefferson drew a line 9.5 inches long. Brittany drew a line 10 times as long. What is the difference in length between the two lines?<\/p>\n

Answer:
\nThe difference in length between the two lines = 85.5 inches.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJefferson drew a line 9.5 inches long.
\nBrittany drew a line 10 times as long.
\n9.5 x 10 = 95.
\n95 – 9.5 = 85.5.
\nso the difference in length between the two lines = 85.5 inches.<\/p>\n

Question 24.
\nConstruct Arguments<\/strong> Jos\u00e9 ran 2.6 miles. Pavel ran 2.60 miles. Who ran farther? Explain your reasoning.<\/p>\n

Answer:
\nJose and Pavel ran the same.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJos\u00e9 ran 2.6 miles. Pavel ran 2.60 miles.
\n2.6 is equal to 2.60.
\nso Jose and Pavel ran the same.<\/p>\n

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

Question 25.
\nChoose all equations that are true.
\n\"Envision 4.82 \u00d7 1,000 = 482,000
\n\"Envision 4.82 \u00d7 102<\/sup> = 482
\n\"Envision 482 \u00d7 101<\/sup> = 48.2
\n\"Envision 482 \u00d7 103<\/sup> = 482
\n\"Envision 48.2 \u00d7 104<\/sup> = 4,820<\/p>\n

Answer:
\n4.82 x 100 = 482.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe equations are:
\n4.82 x 1000 = 482000.
\n4.82 x 10 = 482.
\n482 x 1000 = 482.
\n48.2 x 10000 = 4820.
\nso the equation that is true is 4.82 x 100 = 482.<\/p>\n

Question 26.
\nChoose all equations that are true when 102 is placed in the box.
\n\"Envision o 37 = \"Envision \u00d7 0.37 0
\n\"Envision 0.37 = \"Envision \u00d7 0.037
\n\"Envision 0370 = \"Envision \u00d7 3.7
\n\"Envision 0.37 = \"Envision \u00d7 3.7
\n\"Envision 3.7 = \"Envision \u00d7 0.037<\/p>\n

Answer:
\nNone of the equations are true.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n37 x 102 = 0.370.
\n0.37 x 102 = 0.037.
\n0370 x 102 = 3.7.
\n3.7 x 102 = 0.037.
\nso none of the equations are true.<\/p>\n

Lesson 4.2 Estimate the Product of a Decimal and a Whole Number<\/h2>\n

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

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

Renee needs 32 strands of twine for an art project. Each strand must be 1.25 centimeters long. About how many centimeters of twine does she need? Solve this problem any way you choose!<\/p>\n

Answer:
\nThe centimeters of twine does she need = 40 cm.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nRenee needs 32 strands of twine for an art project.
\nEach strand must be 1.25 centimeters long.
\n32 x 1.25 = 40.
\nso the centimeters of twine does she need = 40 cm.<\/p>\n

Generalize<\/strong> How can you relate what you know about estimating with whole numbers to estimating with decimals? Show
\nyour work!
\n\"Envision<\/p>\n

Look Back!<\/strong> Is your estimate an overestimate or an underestimate? How can you tell?<\/p>\n

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

Essential Question<\/strong>
\nWhat Are Some Ways to Estimate Products of Decimals and Whole Numbers?<\/p>\n

A.<\/strong>
\nA wedding planner needs to buy 16 pounds of sliced cheddar cheese. About how much will the cheese cost?
\n\"Envision<\/p>\n

B.<\/strong>
\nOne Way<\/strong>
\nRound each number to the nearest dollar and nearest ten.
\n\"Envision
\n$2 \u00d7 20 = $40
\nThe cheese will cost about $40.<\/p>\n

C.<\/strong>
\nAnother Way<\/strong>
\nUse compatible numbers that you can multiply mentally.
\n\"Envision
\n$2 \u00d7 15 = $30
\nThe cheese will cost about $30.<\/p>\n

Convince Me!<\/strong> Reasoning<\/strong> About how much money would 18 pounds of cheese cost if the price is $3.95 per pound? Use two different ways to estimate the product. Are your estimates overestimates or underestimates? Explain.<\/p>\n

Another Example<\/strong>
\nManuel walks a total of 0.75 mile to and from school each day. If there have been 105 school days so far this year, about how many miles has he walked in all?
\nRound to the nearest whole number.
\n\"Envision
\nUse compatible numbers.
\n\"Envision
\nBe sure to place the decimal point correctly.
\n\"Envision<\/p>\n

Both methods provide reasonable estimates of how far Manuel has walked.<\/p>\n

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

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

Question 1.
\nNumber Sense<\/strong> There are about 20 school days in a month. In the problem above, about how many miles does Manuel walk each month? Write an equation to show your work.<\/p>\n

Answer:
\nThe number of miles does Manuel walks each month = 16.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThere are about 20 school days in a month.
\n0.75 x 20.
\n0.8 x 20 = 16.
\nso the number of miles does Manuel walks each month = 16.<\/p>\n

Question 2.
\nWithout multiplying, which estimate in the Another example do you think is closer to the exact answer? Explain your reasoning<\/p>\n

Answer:
\nThe number of miles does Manuel walks each month = 16.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThere are about 20 school days in a month.
\n0.75 x 20.
\n0.8 x 20 = 16.
\nso the number of miles does Manuel walks each month = 16.<\/p>\n

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

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

Question 3.
\n0.87 \u00d7 112<\/p>\n

Answer:
\nThe product is 112.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.87 and 112.
\n0.87 x 112.
\n0.8 is equal to 1.
\n112 x 1 = 112.
\nso the product is 112.<\/p>\n

Question 4.
\n104 \u00d7 0.33<\/p>\n

Answer:
\nThe product is 52.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 104 and 0.33.
\n104 x 0.33.
\n0.33 is equal to 0.5.
\n104 x 0.5 = 52.
\nso the product is 52.<\/p>\n

Question 5.
\n9.02 \u00d7 80<\/p>\n

Answer:
\nThe product is 720.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 9.02 and 80.
\n9.02 x 80.
\n9.02 is equal to 9.
\n9 x 80 = 720.
\nso the product is 720.<\/p>\n

Question 6.
\n0.54 \u00d7 24<\/p>\n

Answer:
\nThe product is 12.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.54 and 24.
\n0.54 x 24.
\n0.54 is equal to 0.5.
\n0.5 x 24 = 12.
\nso the product is 12.<\/p>\n

Question 7.
\n33.05 \u00d7 200<\/p>\n

Answer:
\nThe product is 6600.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 33.05 and 200.
\n33.05 x 200.
\n33.05 is equal to 33.
\n33 x 200 = 6600.
\nso the product is 6600.<\/p>\n

Question 8.
\n0.79 \u00d7 51<\/p>\n

Answer:
\nThe product is 51.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.70 and 51.
\n0.7 x 51.
\n0.7 is equal to 1.
\n51 x 1 = 51.
\nso the product is 51.<\/p>\n

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

In 9-16, estimate each product.<\/p>\n

Question 9.
\n0.12 \u00d7 105<\/p>\n

Answer:
\nThe product is 10.5.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.12 and 105.
\n0.12 x 105.
\n0.12 is equal to 0.1.
\n105 x 0.1 = 10.5.
\nso the product is 10.5.<\/p>\n

Question 10.
\n45.3 \u00d7 4<\/p>\n

Answer:
\nThe product is 180.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 45.3 and 4.
\n45.3 x 4.
\n45.3 is equal to 45.
\n45 x 4 = 180.
\nso the product is 180.<\/p>\n

Question 11.
\n99.2 \u00d7 82<\/p>\n

Answer:
\nThe product is 8118.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 99.2 and 82.
\n99.2 x 82.
\n99.2 is equal to 99.
\n99 x 82 = 8118.
\nso the product is 8118.<\/p>\n

Question 12.
\n37 \u00d7 0.93<\/p>\n

Answer:
\nThe product is 37.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 37 and 0.93.
\n37 x 0.93.
\n0.93 is equal to 1.
\n37 x 1 = 37.
\nso the product is 37.<\/p>\n

Question 13.
\n1.67 \u00d7 4<\/p>\n

Answer:
\nThe product is 8.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 1.67 and 4.
\n1.67 x 4.
\n1.67 is equal to 2.
\n4 x 2 = 8.
\nso the product is 8.<\/p>\n

Question 14.
\n3.2 \u00d7 184<\/p>\n

Answer:
\nThe product is 552.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 3.2 and 184.
\n3.2 x 184.
\n3.2 is equal to 3.
\n184 x 3 = 552.
\nso the product is 552.<\/p>\n

Question 15.
\n12 \u00d7 0.37<\/p>\n

Answer:
\nThe product is 3.6.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 12 and 0.3.
\n0.3 x 12.
\n0.3 is equal to 0.3.
\n12 x 0.3 = 3.6.
\nso the product is 3.6.<\/p>\n

Question 16.
\n0.904 \u00d7 75<\/p>\n

Answer:
\nThe product is 75.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.904 and 75.
\n0.904 x 75.
\n0.9 is equal to 1.
\n75 x 1 = 75.
\nso the product is 75.<\/p>\n

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

Question 17.
\nAbout how much money does Stan need to buy 5 T-shirts and 10 buttons?<\/p>\n

Answer:
\nThe cost to buy 5 T-shirts and 10 buttons = $82.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe cost of a button is $1.95.
\nthe cost of the T-shirt is $12.50.
\n1.95 x 10 = 19.5.
\n12.50 x 5 = 62.5.
\n19.5 + 62.5 = 82.
\nso the cost to buy 5 T-shirts and 10 buttons = $82.<\/p>\n

\"Envision<\/p>\n

Question 18.
\nJoseph buys a pair of shorts for $17.95 and 4 T-shirts. About how much money does he spend?<\/p>\n

Answer:
\nThe amount of money he spends = $67.95.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJoseph buys a pair of shorts for $17.95 and 4 T-shirts.
\n$12.50 x 4 = 50.
\n$17.95 + 50 = 67.95.
\nso the money he spend = $67.95.<\/p>\n

Question 19.
\nMarcy picked 18.8 pounds of peaches at the pick-your-own orchard. Each pound costs $1.28. About how much did Marcy pay for the peaches? Write an equation to model your work.<\/p>\n

Answer:
\nThe amount did Marcy pay for the peaches = $24.064.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nMarcy picked 18.8 pounds of peaches at the pick-your-own orchard.
\nEach pound costs $1.28.
\n18.8 x 1.28 = 24.064.
\nso the amount did Marcy pay for the peaches = $24.064.<\/p>\n

Question 20.
\nBe Precise Joshua had $20. He spent $4.58 on Friday, $7.43 on Saturday, and $3.50 on Sunday. How much money does he have left? Show how you found the answer.<\/p>\n

Answer:
\nThe money does he have left = $15.51.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nBe Precise Joshua had $20.
\nHe spent $4.58 on Friday.
\n$7.43 on Saturday, and $3.50 on Sunday.
\n4.58 + 7.43 + 3.50 = 15.51.
\nso the money does he have left = $15.51.<\/p>\n

Question 21.
\nHigher Order Thinking<\/strong> Ms. Webster works 4 days a week at her office and 1 day a week at home. The route to Ms. Webster’s office is 23.7 miles. The route home is 21.8 miles. About how many miles does she drive for work each week? Explain how you found your answer.<\/p>\n

Answer:
\nThe number of miles does she drive for work each week = $116.6.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nMs. Webster works 4 days a week at her office and 1 day a week at home.
\nThe route to Ms. Webster’s office is 23.7 miles.
\nThe route home is 21.8 miles.
\n23.7 x 4 = 94.8.
\n21.8 x 1 = 21.8.
\n94.8 + 21.8 = 116.6
\nso the number of miles does she drive for work each week = $116.6.<\/p>\n

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

Question 22.
\nRounding to the nearest tenth, which of the following give an underestimate?
\n\"Envision 39.45 \u00d7 1.7
\n\"Envision 27.54 \u00d7 0.74
\n\"Envision 9.91 \u00d7 8.74
\n\"Envision 78.95 \u00d7 1.26
\n\"Envision 18.19 \u00d7 2.28<\/p>\n

Answer:
\nThe equations are 39.45 x 1.7 and 27.54 x 0.74.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe equations are:
\n39.45 x 1.7 = 67.065.
\n27.54 x 0.74 = 20.3796.
\n9.91 x 8.74 = 86.6134.
\n78.95 x 1.26 = 99.477.
\n18.19 x 2.28 = 41.4732.<\/p>\n

Question 23.
\nRounding to the nearest whole number, which of the following give an overestimate?
\n\"Envision 11.6 \u00d7 9.5
\n\"Envision 4.49 \u00d7 8.3
\n\"Envision 12.9 \u00d7 0.9
\n\"Envision 0.62 \u00d7 1.5
\n\"Envision 8.46 \u00d7 7.38<\/p>\n

Answer:
\nThe equation is 8.46 x 7.38.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe equations are:
\n11.6 x 9.5 = 110.2.
\n4.49 x 8.3 = 37.267.
\n12.9 x 0.9 = 11.61.
\n0.62 x 1.5 = 0.93.
\n8.46 x 7.38 = 62.4348.<\/p>\n

Lesson 4.3 Use Models to Multiply a Decimal and a Whole Number<\/h3>\n

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

Solve & Share<\/strong>
\nMara has 4 garden plots. Each is 0.7 acre in area. What is the total area of the garden plots? Use objects or the grids below to show your work.<\/p>\n

How can you represent multiplying a decimal and a whole number?
\n\"Envision<\/p>\n

\"Envision
\nLook Back! Critique Reasoning<\/strong> Ed says a decimal grid shows 10 tenths. Monica says a decimal grid shows 100 hundredths. Who is correct? Explain.<\/p>\n

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

Essential Question<\/strong> How Can You Model Multiplying a Decimal by a Whole Number?<\/p>\n

A.<\/strong>
\nHow can you use models to find 4 \u00d7 0.36?
\nWhen showing decimals, it is important to establish which type of block represents 1.<\/p>\n

You can use place-value blocks to show multiplication of a decimal by a whole number.
\n\"Envision<\/p>\n

\"Envision<\/p>\n

B.<\/strong>
\nMultiplying 4 \u00d7 0.36 is like combining 4 groups each containing 0.36.
\n\"Envision
\nRegrouping after combining the blocks gives:
\n\"Envision<\/p>\n

\"Envision<\/p>\n

Convince Me! Make Sense and Persevere<\/strong> Bari made a train with 5 cars that are each 1.27 meter long. What is the total length of the train? Use place-value blocks to model the problem. Then find the product using an equation and compare the answers.<\/p>\n

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

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

Question 1.
\nWithout multiplying, is 4 \u00d7 0.36 less than or greater than 4? Explain.<\/p>\n

Answer:
\n4 x 0.36 is greater than 4.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.36 and 4.
\n4 x 0.36 = 1.44.
\n1.44 is greater than 4.
\nso 4 x 0.36 is greater than 4.<\/p>\n

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

In 2-5, find the product. You may use place-value blocks to help.<\/p>\n

Question 2.
\n0.8 \u00d7 4<\/p>\n

Answer:
\nThe product is 3.2.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.8 and 4.
\nmultiply the two numbers.
\n0.8 x 4 = 3.2.
\nso the product is 3.2.<\/p>\n

Question 3.
\n0.7 \u00d7 3<\/p>\n

Answer:
\nThe product is 2.1.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.7 and 3.
\nmultiply the two numbers.
\n0.7 x 3 = 2.1.
\nso the product is 2.1.<\/p>\n

Question 4.
\n0.5 \u00d7 6<\/p>\n

Answer:
\nThe product is 3.0.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.5 and 6.
\nmultiply the two numbers.
\n0.5 x 6 = 3.0.
\nso the product is 3.0.<\/p>\n

Question 5.
\n0.6 \u00d7 5<\/p>\n

Answer:
\nThe product is 3.0.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.6 and 5.
\nmultiply the two numbers.
\n0.6 x 5 = 3.0.
\nso the product is 3.0.<\/p>\n

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

Use or draw place-value blocks to help you model the problem.
\n\"Envision<\/p>\n

In 6 and 7, find the product. Use place-value blocks to help.<\/p>\n

Question 6.
\n0.55 \u00d7 3 = ___<\/p>\n

Answer:
\nThe product is 1.65.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.55 and 3.
\nmultiply the two numbers.
\n0.55 x 3 = 1.65.
\nso the product is 1.65.<\/p>\n

Question 7.
\n___ = 0.45 \u00d7 2<\/p>\n

Answer:
\nThe product is 0.9.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.45 and 2.
\nmultiply the two numbers.
\n0.45 x 2 = 0.9.
\nso the product is 0.9.<\/p>\n

In 8-19, find the product. Use place-value blocks to help.<\/p>\n

Question 8.
\n5 \u00d7 0.5<\/p>\n

Answer:
\nThe product is 2.5.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.5 and 5.
\nmultiply the two numbers.
\n0.5 x 5 = 2.5.
\nso the product is 2.5.<\/p>\n

Question 9.
\n4 \u00d7 0.27<\/p>\n

Answer:
\nThe product is 1.08.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.27 and 4.
\nmultiply the two numbers.
\n0.27 x 4 = 1.08.
\nso the product is 1.08.<\/p>\n

Question 10.
\n6 \u00d7 0.13<\/p>\n

Answer:
\nThe product is 0.78.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.13 and 6.
\nmultiply the two numbers.
\n0.13 x 6 = 0.78.
\nso the product is 0.78.<\/p>\n

Question 11.
\n0.78 \u00d7 5<\/p>\n

Answer:
\nThe product is 3.9.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.78 and 5.
\nmultiply the two numbers.
\n0.78 x 5 = 3.9.
\nso the product is 3.9.<\/p>\n

Question 12.
\n10 \u00d7 0.32<\/p>\n

Answer:
\nThe product is 3.2.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.32 and 10.
\nmultiply the two numbers.
\n0.32 x 10 = 3.2.
\nso the product is 3.2.<\/p>\n

Question 13.
\n6 \u00d7 2.03<\/p>\n

Answer:
\nThe product is 12.18.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 6 and 2.03.
\nmultiply the two numbers.
\n6 x 2.03 = 12.18.
\nso the product is 12.18.<\/p>\n

Question 14.
\n1.35 \u00d7 5<\/p>\n

Answer:
\nThe product is 6.75.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 1.35 and 5.
\nmultiply the two numbers.
\n1.35 x 5 = 6.75.
\nso the product is 6.75.<\/p>\n

Question 15.
\n100 \u00d7 0.12<\/p>\n

Answer:
\nThe product is 12.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 100 and 0.12.
\nmultiply the two numbers.
\n100 x 0.12 = 12.
\nso the product is 12.<\/p>\n

Question 16.
\n4 \u00d7 0.15<\/p>\n

Answer:
\nThe product is 0.6.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.15 and 4.
\nmultiply the two numbers.
\n0.15 x 4 = 0.6.
\nso the product is 0.6.<\/p>\n

Question 17.
\n3 \u00d7 2.5<\/p>\n

Answer:
\nThe product is 7.5.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 3 and 2.5.
\nmultiply the two numbers.
\n3 x 2.5 = 7.5.
\nso the product is 7.5.<\/p>\n

Question 18.
\n0.9 \u00d7 7<\/p>\n

Answer:
\nThe product is 6.3.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.9 and 7.
\nmultiply the two numbers.
\n0.9 x 7 = 6.3.
\nso the product is 6.3.<\/p>\n

Question 19.
\n0.35 \u00d7 3<\/p>\n

Answer:
\nThe product is 1.05.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.35 and 3.
\nmultiply the two numbers.
\n0.35 x 3 = 1.05.
\nso the product is 1.05.<\/p>\n

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

Question 20.
\nA city is building 3 parks in a new subdivision. Each park will be 1.25 acres. How many total acres will the 3 parks be? Use place-value blocks to model the problem if you need help.<\/p>\n

Answer:
\nThe total number of acres will the 3 parks be 3.75 acres.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA city is building 3 parks in a new subdivision.
\nEach park will be 1.25 acres.
\n1.25 x 3 = 3.75.
\nso the total number of acres will the 3 parks be 3.75 acres.<\/p>\n

How is multiplying with decimals like multiplying whole numbers?
\n\"Envision<\/p>\n

Question 21.
\nHigher Order Thinking<\/strong> The city acquired more land next to the subdivision. If it decides to make each park 12.5 acres, how many additional acres would the parks occupy?<\/p>\n

Answer:
\nThe number of additional acres would the parks occupy = 8.75 acres.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe city acquired more land next to the subdivision.
\nIf it decides to make each park 12.5 acres.
\n3.75 – 12.5 = 8.75.
\nso the number of additional acres would the parks occupy = 8.75 acres.<\/p>\n

Question 22.
\nWrite a multiplication equation that matches the shading on the grid.
\n\"Envision<\/p>\n

Answer:
\n2 + 0.4 = 2.4.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthere are 2 hundred blocks.
\n1 + 1 = 2.
\nthere are 4 tens blocks.
\n0.4.
\n2 + 0.4 = 2.4<\/p>\n

Question 23.
\nCritique Reasoning Jen multiplied 9 by 0.989 and got an answer of 89.01. How can you use estimation to show that Jen’s answer is wrong? What mistake do you think she made?<\/p>\n

Answer:
\nYes, the estimation was wrong.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJen multiplied 9 by 0.989 and got an answer of 89.01.
\n0.989 x 9 = 8.901.
\nso the estimation shows that Jen’s answer is wrong.<\/p>\n

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

Question 24.
\nAnita needs 5 pounds of bananas to make banana bread for a bake sale. Each pound of bananas costs $0.50.
\nPart A<\/strong>
\nHow can Anita use place-value blocks to find the total cost of the bananas? What is the total cost?<\/p>\n

Part B<\/strong>
\nHow can Anita use what she knows about whole-number multiplication to check her answer?<\/p>\n

Answer:
\nThe total cost of the bananas = $2.5.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nAnita needs 5 pounds of bananas to make banana bread for a bake sale.
\nEach pound of bananas costs $0.50.
\n$0.50 x 5 = $2.5.
\nso the total cost of the bananas = $2.5.<\/p>\n

Lesson 4.4 Multiply a Decimal and a Whole Number<\/h3>\n

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

A car travels 1.15 kilometers in 1 minute. If it travels at a constant speed, how far will it travel in 3 minutes? in 5 minutes? Solve this problem any way you choose!<\/p>\n

\"Envision<\/p>\n

Answer:
\nThe far will it travel in 3 minutes = 3.45.
\nthe far will it travel in 5 minutes = 5.75.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA car travels 1.15 kilometers in 1 minute.
\nIf it travels at a constant speed,
\n1.15 x 3 = 3.45.
\n1.15 x 5 = 5.75.<\/p>\n

Generalize<\/strong> You can connect what you know about whole-number multiplication to multiplying a decimal by a whole number.
\n\"Envision<\/p>\n

Look Back!<\/strong> How can addition be used to answer the questions above?<\/p>\n

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

Essential Question<\/strong> How Do You Multiply a Decimal by a Whole Number?<\/p>\n

A.<\/strong>
\nTo raise money for a charity, $0.15 was collected from every ticket sold to a Lions baseball game. If you bought 12 tickets, how much money would go to the charity?
\n\"Envision<\/p>\n

You can multiply 0.15 \u00d7 12 by thinking about 15 \u00d7 12 and using place-value patterns.<\/p>\n

B.<\/strong>
\nOne Way<\/strong>
\nAdd 0.15 twelve times.
\n\"Envision<\/p>\n

C.<\/strong>
\nAnother Way<\/strong>
\nFirst, multiply as you would with whole numbers.
\n\"Envision
\nUse number sense to place the decimal point.
\n\"Envision
\nNotice the digits are the same.
\n\"Envision<\/p>\n

Convince Me! Generalize<\/strong> Here are two similar problems:
\n\"Envision
\nPlace the decimal point correctly in each answer. Explain your thinking.<\/p>\n

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

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

Question 1.
\nWhat is the difference between multiplying a whole number by a decimal and multiplying two whole numbers?<\/p>\n

Answer:
\nThe answer is the same.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n33 x 19 = 627.
\n0.33 x 19 = 627.
\nso the answer is the same.<\/p>\n

Question 2.
\nIf a group bought 24 tickets, how much money would go to charity? Explain how you found your answer.<\/p>\n

Answer:
\nThe money would go to charity = 3.36.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nIf a group bought 24 tickets.
\n24 x 0.14 = 3.36.
\nso the money would go to charity = 3.36.<\/p>\n

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

For 3-8, find each product.<\/p>\n

Question 3.
\n\"Envision<\/p>\n

Answer:
\nThe product is 19.6.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 9.8 and 2.
\nmultiply the two numbers.
\n9.8 x 2 = 19.6.
\nso the product is 19.6.
\n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-4-<\/p>\n

Question 4.
\n\"Envision<\/p>\n

Answer:<\/p>\n

The product is 5.36.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 0.67 and 8.
\nmultiply the two numbers.
\n0.67 x 8 = 5.36.
\nso the product is 5.36.
\n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-4-<\/p>\n

Question 5.
\n34 \u00d7 5.3<\/p>\n

Answer:
\nThe product is 180.2.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 34 and 5.3.
\nmultiply the two numbers.
\n34 x 5.3 = 180.2.
\nso the product is 19.6.<\/p>\n

Question 6.
\n4.6 \u00d7 21<\/p>\n

Answer:
\nThe product is 96.6.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 4.6 and 21.
\nmultiply the two numbers.
\n4.6 x 21 = 96.6.
\nso the product is 96.6.<\/p>\n

Question 7.
\n0.6 \u00d7 15
\nAnswer:
\nThe product is 9.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 0.6 and 15.
\nmultiply the two numbers.
\n0.6 x 15 = 9.
\nso the product is 9.<\/p>\n

Question 8.
\n55 \u00d7 1.1<\/p>\n

Answer:
\nThe product is 60.5.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 55 and 1.1.
\nmultiply the two numbers.
\n55 x 1.1 = 60.5.
\nso the product is 60.5.<\/p>\n

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

For 9-20, find each product.<\/p>\n

Use what you know about whole-number multiplication and place value to help you!
\n\"Envision<\/p>\n

Question 9.
\n\"Envision<\/p>\n

Answer:
\nThe product is 311.4.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 34.6 and 9.
\nmultiply the two numbers.
\n34.6 x 9 = 311.4.
\nso the product is 311.4.
\n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-4-<\/p>\n

Question 10.
\n\"Envision<\/p>\n

Answer:
\nThe product is 1284.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 64.2 and 20.
\nmultiply the two numbers.
\n64.2 x 20 = 1284.
\nso the product is 1284.
\n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-4-<\/p>\n

Question 11.
\n\"Envision<\/p>\n

Answer:
\nThe product is 8.8.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 40 and 0.22.
\nmultiply the two numbers.
\n40 x 0.22 = 8.8.
\nso the product is 8.8.
\n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-4-<\/p>\n

Question 12.
\n\"Envision<\/p>\n

Answer:
\nThe product is 131.1.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 57 and 2.3.
\nmultiply the two numbers.
\n57 x 2.3 = 131.1.
\nso the product is 131.1.
\n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-4-<\/p>\n

Question 13.
\n5.8 \u00d7 11<\/p>\n

Answer:
\nThe product is 63.8.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 5.8 and 11.
\nmultiply the two numbers.
\n5.8 x 11 = 63.8.
\nso the product is 63.8.<\/p>\n

Question 14.
\n56 \u00d7 0.4<\/p>\n

Answer:
\nThe product is 22.4.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 56 and 0.4.
\nmultiply the two numbers.
\n56 x 0.4 = 22.4.
\nso the product is 22.4.<\/p>\n

Question 15.
\n170 \u00d7 0.003<\/p>\n

Answer:
\nThe product is 0.51.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 170 and 0.003.
\nmultiply the two numbers.
\n170 x 0.003 = 0.51.
\nso the product is 0.51.<\/p>\n

Question 16.
\n0.3 \u00d7 99<\/p>\n

Answer:
\nThe product is 29.7.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 0.3 and 99.
\nmultiply the two numbers.
\n0.3 x 99 = 29.7.
\nso the product is 29.7.<\/p>\n

Question 17.
\n26 \u00d7 1.61<\/p>\n

Answer:
\nThe product is 41.86.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 26 and 1.61.
\nmultiply the two numbers.
\n26 x 1.61 = 41.86.
\nso the product is 41.86.<\/p>\n

Question 18.
\n50 \u00d7 0.914<\/p>\n

Answer:
\nThe product is 45.7.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 50 and 0.914.
\nmultiply the two numbers.
\n50 x 0.914 = 45.7.
\nso the product is 45.7.<\/p>\n

Question 19.
\n10.76 \u00d7 100<\/p>\n

Answer:
\nThe product is 1076.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 10.76 and 100.
\nmultiply the two numbers.
\n10.76 x 100 = 1076.
\nso the product is 1076.<\/p>\n

Question 20.
\n2.54 \u00d7 12<\/p>\n

Answer:
\nThe product is 30.48.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 2.54 and 12.
\nmultiply the two numbers.
\n2.54 x 12 = 30.48.
\nso the product is 30.48.<\/p>\n

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

Question 21.
\nenVision\u00ae STEM<\/strong> To meet peak energy demand, an electric power cooperative buys back electricity generated locally. They pay $0.07 per solar-powered kWh (kilowatt-hour). How much money does a school make when it sells back 956 kWh to the cooperative?<\/p>\n

Round and estimate to check for reasonableness.
\n\"Envision<\/p>\n

Answer:
\nThe money does a school makes when it sells back 956 kWh to the cooperative = $66.92.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nan electric power cooperative buys back electricity generated locally.
\nThey pay $0.07 per solar-powered kWh (kilowatt-hour).
\n956 x 0.07 = 66.92.
\nso the money doe a school makes when it sells back 956 kWh to the cooperative = $66.92.<\/p>\n

Question 22.
\nThe airline that Vince is using has a baggage weight limit of 41 pounds. He has two green bags, each weighing 18.4 pounds, and one blue bag weighing 3.7 pounds. Are his bags within the weight limit? Explain.<\/p>\n

Answer:
\nYes, the bags within the weight limit.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe airline that Vince is using has a baggage weight limit of 41 pounds.
\nHe has two green bags, each weighing 18.4 pounds.
\n18.4 + 3.7 = 22.1.
\nso the bags are within the limit.<\/p>\n

Question 23.
\nMichael keeps track of how much time he uses his family’s computer each week for 10 weeks. He created the frequency table with the data he collected. How many hours did Michael spend on the computer?
\n\"Envision<\/p>\n

Answer:
\nThe number of hours did Michael spend on the computer = 17.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nMichael keeps track of how much time he uses his family’s computer each week for 10 weeks.
\n3.5 + 4 + 4.5 + 5 = 17.
\nso the number of hours did Micheal spend on the computer = 17.<\/p>\n

Question 24.
\nCritique Reasoning Sara is multiplying two factors, one is a whole number and one has two decimal places. She says the product could have one decimal place. Is she correct? Give an example and explain your reasoning.<\/p>\n

Answer:
\nYes, she was correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n23 and 23.4.
\n23 x 23.4 = 538.2.
\nso she was correct..<\/p>\n

Question 25.
\nHigher Order Thinking<\/strong> Heather clears a rectangular region in her yard for a garden. If the length is a one-digit whole number and the width is 5.5 meters, what is the least possible area? What is the greatest possible area? Explain how you found your answers.<\/p>\n

Answer:
\nThe least possible area = 60.5.
\nthe greatest possible area = 126.5.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nHeather clears a rectangular region in her yard for a garden.
\nIf the length is a one-digit whole number and the width is 5.5 meters.
\nthe whole number is 11.
\n11 x 5.5 = 60.5.
\nthe whole number is 23.
\n23 x 5.5 = 126.5.
\nso the least possible area = 60.5.<\/p>\n

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

Question 26.
\nWhich of the following equations is NOT true?
\nA. 75 \u00d7 3 = 225
\nB. 75 \u00d7 0.3 = 22.5
\nC. 7.5 \u00d7 3 = 2.25
\nD. 75 \u00d7 0.03 = 2.25<\/p>\n

Answer:
\nOption C is not correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n7.5 x 3 = 22.5.
\nthey have given that
\n7.5 x 3 = 2.25.
\nso option C is not correct.<\/p>\n

Question 27.
\nWhich of the following equations is NOT true?
\nA. 50 \u00d7 12 = 600
\nB. 50 \u00d7 0.12 = 6
\nC. 0.5 \u00d7 12 = 60
\nD. 50 \u00d7 1.2 = 60<\/p>\n

Answer:
\nOption C is not correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n0.5 x 12 = 60.
\nthey have given that
\n0.5 x 12 = 6.
\nso option C is not correct.<\/p>\n

Lesson 4.5 Use Models to Multiply a Decimal and a Decimal<\/h3>\n

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

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

A rectangle has an area of 0.24 square meter. What are some possibilities for the length and width of the rectangle? Tell why. Solve this problem any way you choose. You may use hundredths grids if you like.<\/p>\n

Can both dimensions be greater than 1 meter? Can both dimensions be less than 1 meter? Show your work in the space below.
\n\"Envision<\/p>\n

Look Back! Generalize<\/strong> How did you use what you know about whole numbers and place value to find the dimensions that worked?<\/p>\n

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

Essential Question<\/strong>
\nHow Can You Model Decimal Multiplication?<\/p>\n

A.<\/strong>
\nA farmer has a square field that is 1 mile wide by 1 mile long. Her irrigation system can water the northern 0.5 mile of her field. If her tomatoes are planted in a strip 0.3 mile wide, what is the area of her watered tomatoes?
\n\"Envision<\/p>\n

B.<\/strong>
\nThis problem can be shown on a hundredths grid with each side representing 1 mile. The tomato area is 0.3 mile wide, so shade the first 3 columns red. The watered area is the top 0.5 miles, so shade the top 5 rows blue.
\n\"Envision
\nThe area of the watered tomatoes is the pink area where the shading overlaps.
\n\"Envision<\/p>\n

C.<\/strong>
\nThis area can be written as a product of decimals.
\n0.3 \u00d7 0.5 = 0.15
\nThere is 0.15 square miles of watered tomatoes.
\nBecause both factors are less than 1, the product is less than either factor.<\/p>\n

Convince Me! Be Precise<\/strong> Use the double hundredths grid to model 0.7 \u00d7 1.6. What does the length of each side of a hundredths grid represent? Explain how to find the product.
\n\"Envision<\/p>\n

Answer:
\nEach side of the hundredths grid represents = 2.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n0.7 x 1.6.
\n1.12.
\nso each side of the hundredths grid represents = 2.<\/p>\n

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

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

Question 1.
\nWrite a multiplication equation to match the model.
\n\"Envision<\/p>\n

Answer:
\n0.18 x 0.20 = 0.036.<\/p>\n

Explanation:
\nIn the above-given question,
\nthe grid represents the
\n0.18 and 0.20.
\n0.18 x 0.20 = 0.036.<\/p>\n

Question 2.
\nExplain why 2.7 is not a reasonable answer for 0.3 \u00d7 0.9. What is the correct answer?<\/p>\n

Answer:
\nThe correct answer is 0.27.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 0.3 and 0.9.
\n0.3 x 0.9 = 0.27.
\nso 2.7 is wrong.<\/p>\n

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

In 3 and 4, shade the hundredths grids to find the product.<\/p>\n

Question 3.
\n0.7 \u00d7 0.8
\n\"Envision<\/p>\n

Answer:
\nThe product is 0.56.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 0.7 and 0.8.
\nmultiply the numbers.
\n0.7 x 0.8 = 0.56.
\nso the product is 0.56.<\/p>\n

Question 4.
\n0.1 \u00d7 2.1
\n\"Envision<\/p>\n

Answer:
\nThe product is 0.21.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 0.1 and 2.1.
\nmultiply the numbers.
\n0.1 x 2.1 = 0.21.
\nso the product is 0.21.<\/p>\n

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

In 5-8, shade the hundredths grids to find the product.<\/p>\n

Remember<\/strong> that the area where the shading overlaps represents the product.
\n\"Envision<\/p>\n

Question 5.
\n0.4 \u00d7 0.5
\n\"Envision<\/p>\n

Answer:
\nThe product is 0.2.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 0.4 and 0.5.
\nmultiply the numbers.
\n0.4 x 0.5 = 0.2.
\nso the product is 0.2.<\/p>\n

Question 6.
\n0.3 \u00d7 0.7
\n\"Envision<\/p>\n

Answer:
\nThe product is 0.21.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 0.7 and 0.3.
\nmultiply the numbers.
\n0.7 x 0.3 = 0.21.
\nso the product is 0.21.<\/p>\n

Question 7.
\n0.5 \u00d7 1.7
\n\"Envision<\/p>\n

Answer:
\nThe product is 0.85.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 0.5 and 1.7.
\nmultiply the numbers.
\n0.5 x 1.7 = 0.85.
\nso the product is 0.85.<\/p>\n

Question 8.
\n0.6 \u00d7 1.2
\n\"Envision<\/p>\n

Answer:
\nThe product is 0.72.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 0.6 and 1.2.
\nmultiply the numbers.
\n0.6 x 1.2 = 0.72.
\nso the product is 0.72.<\/p>\n

In 9-16, find the product. You may use grids to help.<\/p>\n

Question 9.
\n0.2 \u00d7 0.8<\/p>\n

Answer:
\nThe product is 0.16.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 0.2 and 0.8.
\nmultiply the numbers.
\n0.2 x 0.8 = 0.16.
\nso the product is 0.16.<\/p>\n

Question 10.
\n2.4 \u00d7 0.7<\/p>\n

Answer:
\nThe product is 1.68.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 2.4 and 0.7.
\nmultiply the numbers.
\n0.7 x 2.4 = 1.68.
\nso the product is 1.68.<\/p>\n

Question 11.
\n3.9 \u00d7 0.4<\/p>\n

Answer:
\nThe product is 1.56.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 3.9 and 0.4.
\nmultiply the numbers.
\n3.9 x 0.4 = 1.56.
\nso the product is 1.56.<\/p>\n

Question 12.
\n0.5 \u00d7 0.7<\/p>\n

Answer:
\nThe product is 0.35.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 0.7 and 0.5.
\nmultiply the numbers.
\n0.7 x 0.5 = 0.35.
\nso the product is 0.35.<\/p>\n

Question 13.
\n0.9 \u00d7 0.1<\/p>\n

Answer:
\nThe product is 0.09.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 0.9 and 0.1.
\nmultiply the numbers.
\n0.9 x 0.1 = 0.09.
\nso the product is 0.09.<\/p>\n

Question 14.
\n0.2 \u00d7 1.5<\/p>\n

Answer:
\nThe product is 0.3.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 0.2 and 1.5.
\nmultiply the numbers.
\n0.2 x 1.5 = 0.3.
\nso the product is 0.3.<\/p>\n

Question 15.
\n0.6 \u00d7 0.6<\/p>\n

Answer:
\nThe product is 0.36.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 0.6 and 0.6.
\nmultiply the numbers.
\n0.6 x 0.6 = 0.36.
\nso the product is 0.36.<\/p>\n

Question 16.
\n2.8 \u00d7 0.3<\/p>\n

Answer:
\nThe product is 0.84.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 2.8 and 0.3.
\nmultiply the numbers.
\n2.8 x 0.3 = 0.84.
\nso the product is 0.84.<\/p>\n

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

Question 17.
\nModel with Math<\/strong> Write a multiplication equation to represent this decimal model.
\n\"Envision<\/p>\n

Answer:<\/p>\n

Question 18.
\nHigher Order Thinking<\/strong> explain why 3.4 \u00d7 0.5 has only one decimal place in the product.<\/p>\n

Answer:
\nYes, it has only one decimal point.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n3.4 and 0.5.
\n3.4 x 0.5 = 1.7.
\nso it has only one decimal place in the product.<\/p>\n

Question 19.
\nJack’s bookshelf has 6 shelves. Each shelf can hold 12 books. He has already placed 54 books on the shelves. How many more books can the bookshelf hold?<\/p>\n

Answer:
\nThe number of books can the bookshelf can hold = 9.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJack’s bookshelf has 6 shelves.
\nEach shelf can hold 12 books.
\nHe has already placed 54 books on the shelves.
\n54 \/ 6 = 9.
\nso the number of books can the bookshelf can hold = 9.<\/p>\n

Question 20.
\nNumber Sense<\/strong> Write a number that has a 6 in the thousandths place, a 5 in the hundredths place, and a 0 in the tenths place. Then write a number less than your number and a number greater than your number.<\/p>\n

Answer:
\nThe number is 65302.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nWrite a number that has a 6 in the thousandths place,
\na 5 in the hundredths place, and a 0 in the tenths place.
\nthe number is 65302.
\nthe number is greater than 65322.
\nthe number is less than 65301.<\/p>\n

Question 21.
\nIf you multiply two decimals less than 1, can you predict whether the product will be less than or greater than either of the factors? Explain.<\/p>\n

Answer:
\nIt is less than the factors.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nIf you multiply two decimals less than 1.
\n0.4 x 0.3 = 0.12.
\nit is less than the factors.<\/p>\n

Question 22.
\nJudy claims that she can find 0.5 \u00d7 2.4 by dividing 2.4 into two equal parts. Is she correct? Draw a decimal model to explain your answer.<\/p>\n

Answer:
\nYes, she was correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n0.5 and 2.4.
\n0.5 x 2.4 = 1.2.
\n1.2 + 1.2 = 2.4.
\nso she was correct.<\/p>\n

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

Question 23.
\nFind two numbers that you can multiply to get a product of 0.54. Write the numbers in the box.
\n\"Envision<\/p>\n

Answer:
\nThe numbers are 0.6 and 0.9.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe product is 0.54.
\n0.6 x 0.9 = 0.54.
\nso the numbers are 0.6 and 0.9.
\n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-4-<\/p>\n

Lesson 4.6 Multiply Decimals Using Partial Products
\nActivity<\/strong><\/p>\n

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

Julie has 0.5 of her backyard set up for growing vegetables. Of the vegetable area, 0.4 has bell peppers in it. What part of the backyard contains bell peppers?<\/p>\n

\"Envision
\nYou can use appropriate tools, such as a grid, to model decimal multiplication.<\/p>\n

Look Back!<\/strong> What do you notice about the factors and their product in the above problem?<\/p>\n

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

Essential Question<\/strong> That How Can You Multiply Decimals Using Partial Products?<\/p>\n

A.<\/strong>
\nJune walked 1.7 miles in 1 hour. If she walks at the same rate, how far will she walk in 1.5 hours?
\n\"Envision
\nYou can use what you know about partial products and whole numbers to model multiplication with decimals.<\/p>\n

B.<\/strong>
\nEstimate first.
\n\"Envision
\nSince 2 is greater than 1.7 and 1.5, 4 is an overestimate.
\n\"Envision<\/p>\n

C.<\/strong>
\nLike with whole numbers, you can use an area model to help break the problem into parts.
\n\"Envision<\/p>\n

D.<\/strong>
\nThe partial products make up the different pieces of the area model.
\n\"Envision
\n1.7 \u00d7 1.5 = 2.55, which is close to the estimate. June will walk 2.55 miles.<\/p>\n

Convince Me!<\/strong> Make Sense and Persevere<\/strong> in the example above, how many miles will June walk in 2.8 hours? Estimate first, then compare your answer to the estimate.<\/p>\n

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

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

Question 1.
\nCarter is filling 6.5-ounce bottles with salsa. He was able to fill 7.5 bottles. How many ounces of salsa did he have? Draw an area model to show the partial products.<\/p>\n

Answer:
\nThe number of ounces<\/p>\n

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

In 2-5, estimate first. Then find each product. Check that your answer is reasonable.<\/p>\n

Question 2.
\n\"Envision<\/p>\n

Answer:
\nThe product is 38.13.<\/p>\n

Explanation:
\nIn the above-given that,
\ngiven that,
\nthe numbers are 9.3 and 4.1.
\nmultiply the numbers.
\n9.3 x 4.1 = 38.13.
\nso the product is 38.13.
\n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-4-<\/p>\n

Question 3.
\n\"Envision<\/p>\n

Answer:
\nThe product is 1.92.<\/p>\n

Explanation:
\nIn the above-given that,
\ngiven that,
\nthe numbers are 3.2 and 0.6.
\nmultiply the numbers.
\n3.2 x 0.6 = 1.92.
\nso the product is 1.92.
\n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-4-<\/p>\n

Question 4.
\n0.7 \u00d7 1.9<\/p>\n

Answer:
\nThe product is 1.33.<\/p>\n

Explanation:
\nIn the above-given that,
\ngiven that,
\nthe numbers are 0.7 and 1.9.
\nmultiply the numbers.
\n0.7 x 1.9 = 1.33.
\nso the product is 1.33.<\/p>\n

Question 5.
\n12.6 \u00d7 0.2<\/p>\n

Answer:
\nThe product is 2.52.<\/p>\n

Explanation:
\nIn the above-given that,
\ngiven that,
\nthe numbers are 12.6 and 0.2.
\nmultiply the numbers.
\n12.6 x 0.2 = 2.52
\nso the product is 2.52.<\/p>\n

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

Question 6.
\nFind 7.5 \u00d7 1.8 using partial products. Draw an area model to show the partial products.
\n\"Envision<\/p>\n

Answer:
\nThe product is 13.5.<\/p>\n

Explanation:
\nIn the above-given that,
\ngiven that,
\nthe numbers are 7.5 and 1.8.
\nmultiply the numbers.
\n7.5 x 1.8 = 13.5.
\nso the product is 13.5.<\/p>\n

In 7-14, estimate first. Then multiply using partial products. Then check that your answer is reasonable.<\/p>\n

Question 7.
\n\"Envision<\/p>\n

Answer:
\n5.2 x 4.6 = 23.92.<\/p>\n

Explanation:
\nIn the above-given that,
\ngiven that,
\nthe numbers are 5.2 and 4.6.
\nmultiply the numbers.
\n5.2 x 4.6 = 23.92.
\nso the product is 23.92.
\n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-4-<\/p>\n

Question 8.
\n\"Envision<\/p>\n

Answer:
\n19.1 x 8.5 = 162.35<\/p>\n

Explanation:
\nIn the above-given that,
\ngiven that,
\nthe numbers are 19.1 and 8.5.
\nmultiply the numbers.
\n19.1 x 8.5 = 162.35.
\nso the product is 162.35.
\n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-4-<\/p>\n

Question 9.
\n\"Envision<\/p>\n

Answer:
\n0.5 x 4.5 = 2.25.<\/p>\n

Explanation:
\nIn the above-given that,
\ngiven that,
\nthe numbers are 0.5 and 4.5.
\nmultiply the numbers.
\n0.5 x 4.5 = 2.25.
\nso the product is 2.25.
\n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-4-<\/p>\n

Question 10.
\n\"Envision<\/p>\n

Answer:
\n8.6 x 0.8 = 6.88.<\/p>\n

Explanation:
\nIn the above-given that,
\ngiven that,
\nthe numbers are 8.6 and 0.8.
\nmultiply the numbers.
\n8.6 x 0.8 = 6.88.
\nso the product is 6.88.
\n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-4-<\/p>\n

Question 11.
\n5.5 \u00d7 0.6<\/p>\n

Answer:
\n5.5 x 0.6 = 3.3.<\/p>\n

Explanation:
\nIn the above-given that,
\ngiven that,
\nthe numbers are 5.5 and 0.6.
\nmultiply the numbers.
\n5.5 x 0.6 = 3.3.
\nso the product is 3.3.<\/p>\n

Question 12.
\n3.5 \u00d7 0.4<\/p>\n

Answer:
\n3.5 x 0.4 = 1.4.<\/p>\n

Explanation:
\nIn the above-given that,
\ngiven that,
\nthe numbers are 3.5 and 0.4.
\nmultiply the numbers.
\n3.5 x 0.4 = 1.4.
\nso the product is 1.4.<\/p>\n

Question 13.
\n6.8 \u00d7 7.2<\/p>\n

Answer:
\n6.8 x 7.2 = 48.96.<\/p>\n

Explanation:
\nIn the above-given that,
\ngiven that,
\nthe numbers are 6.8 and 7.2.
\nmultiply the numbers.
\n6.8 x 7.2 = 48.96.
\nso the product is 48.96.<\/p>\n

Question 14.
\n8.3 \u00d7 6.4<\/p>\n

Answer:
\n8.3 x 6.4 = 53.12.<\/p>\n

Explanation:
\nIn the above-given that,
\ngiven that,
\nthe numbers are 8.3 and 6.4.
\nmultiply the numbers.
\n8.3 x 6.4 = 53.12.
\nso the product is 53.12.<\/p>\n

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

Question 15.
\nenVision\u00ae STEM<\/strong> The gravity of Venus is 0.35 times that of Jupiter. What is the gravity of Venus in relation to Earth’s gravity?<\/p>\n

\"Envision<\/p>\n

Answer:
\nThe gravity of Venus in relation to Earth’s gravity = 0.91.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe gravity of Venus is 0.35 times that of Jupiter.
\nthe gravity of the mercury = 0.39.
\nthe gravity of Neptune = 1.22.
\nthe gravity of Jupiter = 2.6.
\n2.6 x 0.35 = 0.91.
\nso the gravity of venus in relation to Earth’s gravity = 0.91.<\/p>\n

Question 16.
\nAbout how many times as great is Jupiter’s relative surface gravity as Neptune’s relative surface gravity?<\/p>\n

Answer:
\nThe number of times as great is Jupiter’s relative surface gravity as Neptune’s relative surface gravity = 1 time.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe gravity of Neptune = 1.22.
\nthe gravity of Jupiter = 2.6.
\n1.22 – 2.6 = 1.38.
\n1.38 is equal to 1.<\/p>\n

Question 17.
\nOne quart of water weighs about 2.1 pounds. There are 4 quarts in a gallon. How much does a gallon of water weigh?
\n\"Envision<\/p>\n

Answer:
\nThe gallon of water weighs = galloons.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nOne quart of water weighs about 2.1 pounds.
\nThere are 4 quarts in a gallon.
\n2.1 x 4 = 9.6.
\nso the gallon of water weighs = 9.6 galloons.<\/p>\n

Question 18.
\nIsaac bought three packages of nuts. He bought one package of peanuts that weighed 3.07 pounds. He also bought two packages of pecans that weighed 1.46 pounds and 1.5 pounds. Did the peanuts or the pecans weigh more? How much more?<\/p>\n

Answer:
\nThe peanuts weigh more.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nIsaac bought three packages of nuts.
\nHe bought one package of peanuts that weighed 3.07 pounds.
\nalso bought two packages of pecans that weighed 1.46 pounds and 1.5 pounds.
\n1.46 + 1.5 = 2.96.
\n3.07 is greater than 2.96.
\nso the peanuts weigh more.<\/p>\n

Question 19.
\nMake Sense and Persevere<\/strong> How does estimation help you place the decimal point in a product correctly? Explain your reasoning.<\/p>\n

Answer:<\/p>\n

Question 20.
\nHigher Order Thinking<\/strong> The area of Dimitri’s table top is a whole number of square feet. Could the length and width be decimal numbers each with one decimal place? Explain your answer.<\/p>\n

Answer:
\nYes, the answer is correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nfor example:
\n2.6 is the length.
\n3.4 is the width.
\narea = l x w.
\narea = 2.6 x 3.4.
\narea = 8.84.<\/p>\n

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

Question 21.
\nJoy drinks 4.5 bottles of water per day. Each bottle contains 16.5 fluid ounces. How many fluid ounces of water does she drink per day?
\nA. 20.10 fluid Ounces
\nB. 64.00 fluid ounces
\nC. 74.25 fluid Ounces
\nD. 82.50 fluid Ounces<\/p>\n

Answer:
\nOption C is correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJoy drinks 4.5 bottles of water per day.
\nEach bottle contains 16.5 fluid ounces.
\n4.5 x 16.5 = 74.25.
\nso option C is correct.<\/p>\n

Question 22.
\nOne square mile equals 2.6 square kilometers. How many square kilometers are in 14.4 square miles?
\nA. 11.52 square kilometers
\nB. 17.00 square kilometers
\nC. 37.44 square kilometers
\nD. 86.40 square kilometers<\/p>\n

Answer:
\nOption C is correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nOne square mile equals 2.6 square kilometers.
\n14.4 x 2.6 = 37.44.
\nso the number of square kilometers are in 14.4 is 37.44 miles.<\/p>\n

Lesson 4.7 Use Properties to Multiply Decimals<\/h3>\n

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

Solve & Share<\/strong>
\nThe weight of a small bag of raisins is 0.3 times the weight of a large bag. The large bag weighs 0.8 pound. What is the weight of the small bag? Solve this problem any way you choose.<\/p>\n

Answer:
\nThe weight of the small bag = 0.24.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe weight of a small bag of raisins is 0.3 times the weight of a large bag.
\nThe large bag weighs 0.8 pounds.
\n0.8 x 0.3 = 0.24.
\nso the weight of the small bag = 0.24.<\/p>\n

You can estimate whether the answer is greater than or less than 0.5 pound.
\n\"Envision<\/p>\n

Look Back! Look for Relationships How is solving this problem like finding the product of 3 and 8? How is it different?<\/p>\n

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

Essential Question<\/strong> How Can You Use Properties to Multiply Decimals?<\/p>\n

A.<\/strong>
\nEntries for a poster contest must be 0.5 m2 or smaller. Can Jemelle enter her poster?
\n\"Envision<\/p>\n

Use what you know about decimals and properties to multiply 0.6 \u00d7 0.9.
\n\"Envision<\/p>\n

B.<\/strong>
\nStep 1<\/strong>
\nRewrite the multiplication expression.
\n0.6 \u00d7 0.9 = (6 \u00d7 0.1) \u00d7 (9 \u00d7 0.1)
\nRearrange the factors using the Associative and Commutative Properties.
\n(6 \u00d7 0.1) \u00d7 (9 \u00d7 0.1) = (6 \u00d7 9) \u00d7 (0.1 \u00d7 0.1)<\/p>\n

C.<\/strong>
\nStep 2<\/strong>
\nMultiply the whole numbers. Multiply the decimals. Write the product.
\n(6 \u00d7 9) \u00d7 (0.1 \u00d7 0.1) = 54 \u00d7 0.01 = 0.54
\nOne tenth of one tenth is one hundredth. 0.1 \u00d7 0.1 = 0.01.
\n\"Envision
\n0.54 > 0.5,
\nso Jemelle cannot enter her poster.<\/p>\n

Convince Me! Use Structure<\/strong> Tyler explained how he multiplies 0.7 \u00d7 0.2. \u201cI multiply 7 \u00d7 2 = 14. I know that a tenth times a tenth is a hundredth, so I use hundredths to write the product. The product is 0.14.” Use properties to show that Tyler is correct.<\/p>\n

Answer:
\nYes, Tailor was correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nTyler explained how he multiplies 0.7 \u00d7 0.2. \u201cI multiply 7 \u00d7 2 = 14.
\n0.7 x 0.2 = 0.14.
\nso Tailor was correct.<\/p>\n

Another example<\/strong>
\nA slice of bread has 1.25 grams of fat. How many grams of fat are in 1.5 slices?
\n1.25 \u00d7 1.5 =
\n= (125 \u00d7 0.01) (15 \u00d7 0.1)
\n= (125 \u00d7 15) \u00d7 (0.01 \u00d7 0.1)
\n= 1,875 \u00d7 0.001
\n= 1.875
\n\"Envision
\nThe picture shows that one tenth of one hundredth is one thousandth. 0.1 \u00d7 0.01 = 0.001
\n\"Envision
\nThere are 1.875 grams of fat in 1.5 slices of bread.<\/p>\n

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

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

Question 1.
\nMason is multiplying (3 \u00d7 5) \u00d7 (0.1 \u00d7 0.1). What decimal multiplication problem is he solving?<\/p>\n

Answer:
\n3 x 5 x 0.1 x 0.1 = 0.15.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nMason is multiplying (3 x 5) x (0.1 x 0.1).
\n15 x (0.1 x 0.1).
\n15 x 0.01.
\n0.15.<\/p>\n

Question 2.
\nComplete Mason’s work to find the product.<\/p>\n

Answer:
\n3 x 5 x 0.1 x 0.1 = 0.15.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nMason is multiplying (3 x 5) x (0.1 x 0.1).
\n15 x (0.1 x 0.1).
\n15 x 0.01.
\n0.15.<\/p>\n

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

In 3-6, use properties to find each product.<\/p>\n

Question 3.
\n0.3 \u00d7 0.7<\/p>\n

Answer:
\n0.3 x 0.7 = 0.21.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 0.3 and 0.7.
\n0.3 x 0.7.
\n3 x 0.1 = 0.3.
\n7 x 0.1 = 0.7.
\n(3 x 7) x (0.1 x 0.1).
\n(21) x (0.01).
\n0.21.<\/p>\n

Question 4.
\n0.63 \u00d7 2.8<\/p>\n

Answer:
\n0.63 x 2.8 = 17.64.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 0.63 and 2.8.
\n0.63 x 2.8.
\n63 x 0.1 = 0.63.
\n28 x 0.1 = 0.7.
\n(63 x 28) x (0.1 x 0.1).
\n(1764) x (0.01).
\n17.64.<\/p>\n

Question 5.
\n2.6 \u00d7 1.4<\/p>\n

Answer:
\n2.6 x 1.4 = 3.64.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 2.6 and 1.4.
\n2.6 x 1.4.
\n2.6 x 0.1 = 2.6.
\n1.4 x 0.1 = 1.4.
\n(2.6 x 1.4) x (0.1 x 0.1).
\n(3.64) x (0.01).
\n3.64.<\/p>\n

Question 6.
\n4.5 \u00d7 0.08<\/p>\n

Answer:
\n4.5 x 0.08 = 3.6.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 0.3 and 0.7.
\n4.5 x 0.08.
\n45 x 0.1 = 4.5.
\n8 x 0.01 = 0.08.
\n(45 x 8) x (0.1 x 0.01).
\n(360) x (0.01).
\n3.6.<\/p>\n

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

In 7-15, find each product.<\/p>\n

Question 7.
\n0.6 \u00d7 0.2<\/p>\n

Answer:
\nThe product is 0.12.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.6 and 0.2.
\nmultiply the two numbers.
\n0.6 x 0.2 = 0.12.<\/p>\n

Question 8.
\n0.33 \u00d7 0.8<\/p>\n

Answer:
\nThe product is 0.264.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.33 and 0.8.
\nmultiply the two numbers.
\n0.33 x 0.8 = 0.264.<\/p>\n

Question 9.
\n1.7 \u00d7 0.22<\/p>\n

Answer:
\nThe product is 0.374.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 1.7 and 0.22.
\nmultiply the two numbers.
\n1.7 x 0.22 = 0.374.<\/p>\n

Question 10.
\n1.8 \u00d7 0.9<\/p>\n

Answer:
\nThe product is 1.62.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.9 and 1.8.
\nmultiply the two numbers.
\n0.9 x 1.8 = 1.62.<\/p>\n

Question 11.
\n0.03 \u00d7 1.6<\/p>\n

Answer:
\nThe product is 0.48.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 1.6 and 0.03.
\nmultiply the two numbers.
\n1.6 x 0.03 = 0.48.<\/p>\n

Question 12.
\n4.2 \u00d7 4.2<\/p>\n

Answer:
\nThe product is 17.64.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 4.2 and 4.2.
\nmultiply the two numbers.
\n4.2 x 4.2 = 17.64.<\/p>\n

Question 13.
\n11.1 \u00d7 0.8<\/p>\n

Answer:
\nThe product is 8.88.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 0.8 and 11.1.
\nmultiply the two numbers.
\n0.8 x 11.1 = 8.88.<\/p>\n

Question 14.
\n1.16 \u00d7 0.4<\/p>\n

Answer:
\nThe product is 0.464.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 1.16 and 0.4.
\nmultiply the two numbers.
\n1.16 x 0.4 = 0.464.<\/p>\n

Question 15.
\n1.6 \u00d7 0.01<\/p>\n

Answer:
\nThe product is 0.016.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 1.6 and 0.01.
\nmultiply the two numbers.
\n1.6 x 0.01 = 0.016.<\/p>\n

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

Question 16.
\nThe total rainfall in March was 3.6 inches. In April, the total rainfall was 1.4 times as much. What was the total rainfall in April?<\/p>\n

Answer:
\nThe total rainfall in April = 5.04.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe total rainfall in March was 3.6 inches.
\nIn April, the total rainfall was 1.4 times as much.
\n3.6 x 1.4 = 5.04.
\nso the total rainfall in April = 5.04.<\/p>\n

Question 17.
\nA newly hatched alligator is 0.5 foot long. An adult alligator is 16.4 times as long. How many feet longer is the adult alligator than the newborn alligator?<\/p>\n

Answer:
\nThe longer is the adult alligator than the newborn alligator = 8.2 feet.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA newly hatched alligator is 0.5 feet long.
\nAn adult alligator is 16.4 times as long.
\n16.4 x 0.5 = 8.2.
\nso the longer is the adult alligator than the newborn alligator = 8.2 feet.<\/p>\n

Question 18.
\nMake Sense and Persevere The Nature Club held a grasshopper jumping contest. The distance Bugmaster jumped is 1.2 times the distance Green Lightning jumped. The distance Top Hopper jumped is 1.5 times the distance Bugmaster jumped. Complete the table to show the distances Bugmaster and Top Hopper jumped.
\n\"Envision<\/p>\n

Answer:
\nThe Bugmaster and Top Hopper jumped = 1.68 feet and 2.1 feet.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe Nature Club held a grasshopper jumping contest.
\nThe distance Bugmaster jumped is 1.2 times the distance green Lightning jumped.
\nThe distance Top Hopper jumped is 1.5 times the distance Bugmaster jumped.
\n1.4 x 1.2 = 1.68.
\n1.4 x 1.5 = 2.1.<\/p>\n

Question 19.
\nAmanda bought a 6-cup bag of shredded cheese for $6.89. She used 2.25 cups to make lasagna and 1.25 cups to make pizza. How much cheese is left?
\nIs there any information that you don’t need to solve this problem?
\n\"Envision<\/p>\n

Answer:
\nThe quantity of cheese left = $3.39.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nAmanda bought a 6-cup bag of shredded cheese for $6.89.
\nShe used 2.25 cups to make lasagna and 1.25 cups to make pizza.
\n2.25 + 1.25 = 3.5.
\n6.89 – 3.5 = 3.39.
\nso the quantity of cheese left = 3.39.<\/p>\n

Question 20.
\nHigher Order Thinking<\/strong> Jodi drew the Eiffel Tower 6.5 inches tall. She thought it was too tall, so she multiplied its height by 0.8. The second drawing was too short, so she multiplied its height by 1.2. Predict whether her last drawing was shorter, the same as, or taller than her first drawing. Check your prediction by finding the height of the last drawing.<\/p>\n

Answer:
\nThe taller than her first drawing = 4.5 inches.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJodi drew the Eiffel Tower 6.5 inches tall.
\nShe thought it was too tall, so she multiplied its height by 0.8.
\nThe second drawing was too short, so she multiplied its height by 1.2.
\n0.8 + 1.2 = 2.
\n6.5 – 2 = 4.5.
\nso the taller than her first drawing = 4.5 inches.<\/p>\n

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

Question 21.
\nWhich expression is equivalent to 0.4 \u00d7 0.3?
\nA. (4 \u00d7 0.01) \u00d7 (3 \u00d7 0.01)
\nB. (4 \u00d7 10) \u00d7 (3 \u00d7 10)
\nC. (4 \u00d7 0.1) \u00d7 (3 \u00d7 0.1)
\nD. (4 \u00d7 0.1) \u00d7 (3 \u00d7 0.01)<\/p>\n

Answer:
\nOption C is correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n0.4 x 0.3 = 0.12.
\n4 x 0.1 = 0.4.
\n3 x 0.1 = 0.3.
\n0.4 x 0.3 = 0.12.
\nso option C is correct.<\/p>\n

Question 22.
\nWhich expression is equivalent to 0.71 \u00d7 2.8?
\nA. (71 \u00d7 28) \u00d7 (0.01 \u00d7 0.1)
\nB. (71 \u00d7 28) \u00d7 (0.1 \u00d7 0.1)
\nC. (0.71 \u00d7 2.8) \u00d7 (0.01 \u00d7 0.1)
\nD. (71 \u00d7 28) \u00d7 (100 \u00d7 10)<\/p>\n

Answer:
\nOption C is correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n0.71 x 2.8 = 1.96.
\n0.71 x 2.8 x 0.01 x 0.1 = 1.96.
\nso option C is correct.<\/p>\n

Lesson 4.8 Use Number Sense to Multiply Decimals<\/h3>\n

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

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

Three students in Ms. Cho’s class wrote the following problems on the board. The correct digits in the products are given, but the decimal point isn’t placed yet. Where should the decimal point go in each product?<\/p>\n

\"Envision<\/p>\n

You can use reasoning to consider the size of each factor when placing the decimal point. Show your work!
\n\"Envision<\/p>\n

Look Back! Generalize<\/strong> If both factors are less than 1, what do you know about their product?<\/p>\n

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

Essential Question<\/strong>
\nHow Can You Use Number Sense Question to Multiply Decimals?<\/p>\n

A.<\/strong>
\nYou have learned how to estimate when multiplying with decimals. You can also use number sense to reason about the relative size of factors and the product.<\/p>\n

You can use number sense to put the decimal point in the correct place.
\n\"Envision<\/p>\n

49.20 \u00d7 0.55 = 2706<\/p>\n

B.<\/strong>
\nThink about the relative size of the factors.
\nMultiplying a number by a decimal less than 1 gives a product less than the other factor. Since 0.55 is less than 1, the product is less than 49.2.
\nSince 0.55 is about one half, the product is about half of 49.2, or about half of 50. So, the decimal point
\n1 should be between the 7 and 0.
\n49.2 \u00d7 0.55 = 27.06<\/p>\n

C.<\/strong>
\nUse number sense to reason about the product.
\nHow can you place the decimal point in the product of the equation below?
\n6.2 \u00d7 5.1 is 3162.
\nNotice that the smallest unit in both factors is a tenth (0.1). Since the product of 0.1 and 0.1 is 0.01, the product of 6.2 and 5.1 will have two decimal places.
\nSo, 6.2 \u00d7 5.1 = 31.62.
\nThis makes sense because 6 times 5 equals 30.
\n\"Envision<\/p>\n

Convince Me! Construct Arguments<\/strong> The decimal point is missing in the answer for each of these problems. Use number sense to decide where the decimal point should be placed. Explain your thinking.
\n54.7 \u00d7 0.53 = 28991
\n54.7 \u00d7 5.3 = 28991<\/p>\n

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

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

Question 1.
\nDescribe the unknown factor.
\n____ \u00d7 5.1 is about 300.<\/p>\n

Answer:
\nThe unknown factor is 58.823.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n300\/5.1 = 58.8.
\n58.8 x 5.1 = 300.
\nthe unknown factor is 58.823.<\/p>\n

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

Question 2.
\nNumber Sense Janelle wrote 23.4 for the product of 7.8 \u00d7 0.3. Use number sense to decide if Janelle placed the decimal point in the correct place in the product. If it is incorrect, give the correct product.<\/p>\n

Answer:
\n7.8 x 0.3 = 2.34.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJanelle wrote 23.4 for the product of 7.8 \u00d7 0.3.
\n7.8 x 0.3 = 2.34.
\nso the product is correct.<\/p>\n

Use number sense to decide where the decimal point belongs in the product.<\/p>\n

Question 3.
\n5 \u00d7 3.4 = 17<\/p>\n

Answer:
\n5 x 3.4 = 17.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 5 and 3.4.
\nmultiply the two numbers.
\n5 x 3.4 = 17.<\/p>\n

Question 4.
\n1922 = 3.1 \u00d7 6.2<\/p>\n

Answer:
\n3.1 x 6.2 = 19.22.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 3.1 and 6.2.
\nmultiply the two numbers.
\n3.1 x 6.2 = 19.22.<\/p>\n

Question 5.
\n0.6 \u00d7 0.4 = 24<\/p>\n

Answer:
\n0.6 x 0.4 = 0.24.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 0.6 and 0.4.
\nmultiply the two numbers.
\n0.6 x 0.4 = 0.24.<\/p>\n

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

In 6-9, the product is shown without the decimal point. Use number sense to place the decimal point correctly.<\/p>\n

Question 6.
\n5.01 \u00d7 3 = 1503<\/p>\n

Answer:
\n5.01 x 3 = 15.03.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 5.01 and 3.
\nmultiply the two numbers.
\n5.01 x 3 = 15.03.<\/p>\n

Question 7.
\n6.22 \u00d7 3 = 1866<\/p>\n

Answer:
\n6.22 x 3 = 18.66.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 6.22 and 3.
\nmultiply the two numbers.
\n6.22 x 3 = 18.66.<\/p>\n

Question 8.
\n81 = 0.9 \u00d7 0.9<\/p>\n

Answer:
\n0.9 x 0.9 = 0.81.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 0.9 and 0.9.
\nmultiply the two numbers.
\n0.9 x 0.9 = 0.81.<\/p>\n

Question 9.
\n1.8 \u00d7 1.9 = 342<\/p>\n

Answer:
\n1.8 x 1.9 = 3.42.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 1.8 and 1.9
\nmultiply the two numbers.
\n1.8 x 1.9 = 3.42.<\/p>\n

In 10-15, tell whether or not the decimal point has been placed correctly in the product. If not, rewrite the product with the decimal point correctly placed.<\/p>\n

Use number sense or estimation to help you!
\n\"Envision<\/p>\n

Question 10.
\n12 \u00d7 4.8 = 57.6<\/p>\n

Answer:
\n12 x 4.8 = 57.6.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 12 and 4.8.
\nmultiply the two numbers.
\n12 x 4.8 = 57.6.<\/p>\n

Question 11.
\n5.2 \u00d7 6.4 = 3.328<\/p>\n

Answer:
\n5.2 x 6.4 = 33.28.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 5.2 and 6.4.
\nmultiply the two numbers.
\n5.2 x 6.4 = 33.28.<\/p>\n

Question 12.
\n6.99 \u00d7 21 = 14.679<\/p>\n

Answer:
\n6.99 x 21 = 146.79.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 6.99 and 21.
\nmultiply the two numbers.
\n6.99 x 21 = 146.79.<\/p>\n

Question 13.
\n6.2 = 0.05 \u00d7 12.4<\/p>\n

Answer:
\n0.05 x 12.4 = 0.62.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 0.05 and 12.4.
\nmultiply the two numbers.
\n0.05 x 12.4 = 0.62.<\/p>\n

Question 14.
\n60.84 = 18 \u00d7 3.38<\/p>\n

Answer:
\n18 x 3.38 = 60.84.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 18 and 3.38.
\nmultiply the two numbers.
\n18 x 3.38 = 60.84.<\/p>\n

Question 15.
\n9.01 \u00d7 91 = 81.991<\/p>\n

Answer:
\n9.01 x 91 = 819.91.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 9.01 and 91.
\nmultiply the two numbers.
\n9.01 x 91 = 819.91.<\/p>\n

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

Question 16.
\nA pig farmer needs 60 square feet to house a sow. Is the pen pictured to the right large enough? Explain your reasoning
\n\"Envision<\/p>\n

Answer:
\nThe pen is not pictured to the right large enough.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA pig farmer needs 60 square feet to house a sow.
\n10.5 x 6.4 = 67.2.
\nso the pen is not pictured to the right large enough.<\/p>\n

Question 17.
\nCritique Reasoning<\/strong> Quincey says that 3 is a good estimate for 3.4 \u00d7 0.09. Is he correct? Why?<\/p>\n

Answer:
\nYes, 3 is a good estimate for 3.4 x 0.09.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n3.4 x 0.09 = 0.306.
\nso 3 is a good estimate for 3.4 x 0.09.<\/p>\n

Question 18.
\nRon bought 2 DVDs for $12.95 each. He spent $25 on magazines. Did he spend more on DVDs or magazines? How much more? Write equations to show your work.<\/p>\n

Answer:
\nHe spends more on DVDs.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nRon bought 2 DVDs for $12.95 each.
\nHe spent $25 on magazines.
\nhe spend more on DVDs.<\/p>\n

Question 19.
\nYou can convert gallons to liters by using a factor of 3.79. That is, 1 gallon is about 3.79 liters. About how many liters are in 37 gallons? Is your answer an underestimate or overestimate? Explain.<\/p>\n

Answer:
\nYes, the answer is an overestimate.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nYou can convert gallons to liters by using a factor of 3.79.
\nThat is, 1 gallon is about 3.79 liters.
\n37 x 3.79 = 140.23.
\nso the answer is overestimated.<\/p>\n

Question 20.
\nHigher Order Thinking<\/strong> Find two factors that would give a product of 0.22.<\/p>\n

Answer:
\nThe two factors are 0.11 and 2.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two factors are 0.11 and 2.
\n0.11 x 2 = 0.22.
\nso the factors are 0.11 and 2.<\/p>\n

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

Question 21.
\nWhich of the following is the missing factor?
\n___ \u00d7 2.3 = 34.73
\nA. 0.151
\nB. 1.51
\nC. 15.1
\nD. 151<\/p>\n

Answer:
\nThe missing factor is 15.1.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n15.1 x 2.3 = 34.73.
\n34.73 \/ 2.3 = 15.1.
\nso the missing factor is 15.1.<\/p>\n

Question 22.
\nWhich two factors would give a product of 7.5?
\nA. 0.3 and 0.25
\nB. 0.3 and 2.5
\nC. 3 and 0.25
\nD. 3 and 2.5<\/p>\n

Answer:
\nOption D is correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n3 x 2.5 = 7.5.
\nso option D is correct.<\/p>\n

Lesson 4.9 Model with Math<\/h3>\n

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

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

Solve&Share<\/strong>
\nSusan is making sandwiches for a picnic. She needs 1.2 pounds of ham, 1.5 pounds of bologna, and 2 pounds of cheese. How much will she spend in all? Solve this problem any way you choose. Use models to help.<\/p>\n

Answer:
\nThe amount he spends in all = 4.7.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nSusan is making sandwiches for a picnic.
\nShe needs 1.2 pounds of ham.
\n1.5 pounds of bologna, and 2 pounds of cheese.
\n1.2 + 1.5 + 2 = 4.7.
\nso the amount he spends in all = 4.7.<\/p>\n

\"Envision<\/p>\n

Thinking Habits<\/strong>
\nBe a good thinker! These questions can help you.
\n\u2022 How can I use math I know to help solve this problem?
\n\u2022 How can I use pictures, objects, or an equation to represent the problem?
\n\u2022 How can I use numbers, words, and symbols to solve the problem?
\n\"Envision<\/p>\n

Look Back!<\/strong> What math did you use to solve this problem?<\/p>\n

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

Essential Question<\/strong>
\nHow Can You Model a Problem with an Equation?<\/p>\n

A.<\/strong>
\nAlex is buying vegetables for dinner. He buys 6 ears of corn, 1.4 pounds of green beans, and 2.5 pounds of potatoes. How much money does he spend?
\n\"Envision<\/p>\n

What do I need to do to solve the problem?
\nI need to find how much money Alex spends on vegetables.<\/p>\n

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

B.<\/strong>
\nHow can I model with math?
\nI can
\n\u2022 use previously learned concepts and skills.
\n\u2022 decide what steps need to be completed to find the final answer
\n\u2022 use an equation to represent and solve this problem.<\/p>\n

C.<\/strong>
\nI will use an equation to represent this situation.
\nLet t be the total cost.
\nt = (6 \u00d7 $0.35) + (1.4 \u00d7 $1.80) + (2.5 \u00d7 $0.70)
\nMultiply with money as you would multiply with decimals.
\n\"Envision
\nNow add the subtotals.
\n$2.10 + $2.52 + $1.75 = $6.37
\nSo, Alex spends $6.37 on vegetables.<\/p>\n

Convince Me!<\/strong> Model with Math<\/strong> Beth buys 3.2 pounds of potatoes and gives the clerk a $5 bill. Write an equation that shows how much change she will get back. Explain how your equation represents this problem.<\/p>\n

Answer:
\nThe change she will get back = 30.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nBeth buys 3.2 pounds of potatoes and gives the clerk a $5 bill.
\n1 pound = 100.
\n1 dollar = 70.
\n3.2 x 100 = 320.
\n5 x 70 = 350.
\n350 – 320 = 30.
\nso the change she will get back = 30.<\/p>\n

Guided Practice<\/strong>
\nModel with Math<\/strong> Jackie downloaded 14 songs priced at $0.99 each and 1 song for $1.29. She had a coupon for $2.50. What was the total amount Jackie paid?<\/p>\n

Answer:
\nThe total amount Jackie paid = $2.28.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJackie downloaded 14 songs priced at $0.99 each and 1 song for $1.29.
\nshe had a coupon for $2.50.
\n0.99 + 1.29 = 2.28.
\nso the total amount Jackie paid = $2.28.<\/p>\n

You can model with math by writing an equation to show how the quantities in the problem are related.
\n\"Envision<\/p>\n

Question 1.
\nWhat do you need to find first?<\/p>\n

Answer:
\nThe total amount Jackie paid = $2.28.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJackie downloaded 14 songs priced at $0.99 each and 1 song for $1.29.
\nshe had a coupon for $2.50.
\n0.99 + 1.29 = 2.28.
\nso the total amount Jackie paid = $2.28.<\/p>\n

Question 2.
\nWrite an equation to represent the problem.<\/p>\n

Answer:
\nThe total amount Jackie paid = $2.28.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJackie downloaded 14 songs priced at $0.99 each and 1 song for $1.29.
\nshe had a coupon for $2.50.
\n0.99 + 1.29 = 2.28.
\nso the total amount Jackie paid = $2.28.<\/p>\n

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

Answer:
\nThe total amount Jackie paid = $2.28.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJackie downloaded 14 songs priced at $0.99 each and 1 song for $1.29.
\nshe had a coupon for $2.50.
\n0.99 + 1.29 = 2.28.
\nso the total amount Jackie paid = $2.28.<\/p>\n

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

Model with Math George bought 2.5 pounds of each type of fruit shown on the sign. What was the total cost of the fruit he bought?<\/p>\n

\"Envision<\/p>\n

Question 4.
\nWhat do you need to find?<\/p>\n

Answer:
\nThe total cost of the fruit he bought = $2.635.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nGeorge bought 2.5 pounds of each type of fruit shown on the sign.
\nthe cost of Apples is $1.30\/lb.
\nthe cost of Grapes is $1.65\/lb.
\nthe cost of Bananas is $0.49\/lb.
\n1.30 + 1.65 + 0.49 = 2.635.
\nso the total cost of the fruit he bought = $2.635.<\/p>\n

Question 5.
\nWrite an equation to represent the problem.<\/p>\n

Answer:
\nThe total cost of the fruit he bought = $2.635.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nGeorge bought 2.5 pounds of each type of fruit shown on the sign.
\nthe cost of Apples is $1.30\/lb.
\nthe cost of Grapes is $1.65\/lb.
\nthe cost of Bananas is $0.49\/lb.
\n1.30 + 1.65 + 0.49 = 2.635.
\nso the total cost of the fruit he bought = $2.635.<\/p>\n

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

Answer:
\nThe total cost of the fruit he bought = $2.635.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nGeorge bought 2.5 pounds of each type of fruit shown on the sign.
\nthe cost of Apples is $1.30\/lb.
\nthe cost of Grapes is $1.65\/lb.
\nthe cost of Bananas is $0.49\/lb.
\n1.30 + 1.65 + 0.49 = 2.635.
\nso the total cost of the fruit he bought = $2.635.<\/p>\n

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

Performance Task<\/strong>
\nCoin Collection<\/strong>
\nTina and Shannon counted the coins in their coin collections. Tina discovered that she had 538 more coins than Shannon. Whose collection is worth more? How much more?<\/p>\n

\"Envision<\/p>\n

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

Answer:
\nYes, she was correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nTina and Shannon counted the coins in their coin collections.
\nTina discovered that she had 538 more coins than Shannon.
\n917 + 100 + 45 + 19 = 1081.
\n488 + 23 + 10 + 22 = 543.
\n1081 – 543 = 538.<\/p>\n

Question 8.
\nReasoning<\/strong> How is finding the total value of the coins in Tina’s collection similar to finding the total value of coins in Shannon’s collection?<\/p>\n

Answer:
\nThe total value of the coins in Tina’s collection is 1081.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nTina and Shannon counted the coins in their coin collections.
\nTina discovered that she had 538 more coins than Shannon.
\n917 + 100 + 45 + 19 = 1081.
\n488 + 23 + 10 + 22 = 543.
\n1081 – 543 = 538.<\/p>\n

Deciding what steps need to be completed to find the final answer can help you model with math.
\n\"Envision<\/p>\n

Question 9.
\nModel with Math<\/strong> Write and solve an equation to represent the total value of the coins in Tina’s collection. Then write and solve an equation to represent the total value of the coins in Shannon’s collection.<\/p>\n

Answer:
\nThe total value of the coins in Shanno’s collection = 543.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nTina and Shannon counted the coins in their coin collections.
\nTina discovered that she had 538 more coins than Shannon.
\n917 + 100 + 45 + 19 = 1081.
\n488 + 23 + 10 + 22 = 543.
\n1081 – 543 = 538.<\/p>\n

Question 10.
\nBe Precise<\/strong> Whose collection is worth more? How much more? Show your work.<\/p>\n

Answer:
\nTina’s collection is worth more.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nTina and Shannon counted the coins in their coin collections.
\nTina discovered that she had 538 more coins than Shannon.
\n917 + 100 + 45 + 19 = 1081.
\n488 + 23 + 10 + 22 = 543.
\n1081 – 543 = 538.<\/p>\n

Topic 4 Fluency Practice<\/h3>\n

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

Find a match<\/strong><\/p>\n

Work with a partner. Point to a clue.
\nRead the clue.
\nLook below the clues to find a match. Write the clue letter in the box above the match.
\nFind a match for every clue.
\n\"Envision<\/p>\n

Clues<\/strong>
\n\"Envision<\/p>\n

\"Envision<\/p>\n

Answer:
\n51 x 63 = 3213.
\n10 x 10 = 100.
\n42 x 11 = 462.
\n20 x 12 = 240.
\n15 x 17 = 255.
\n40 x 23 = 920.
\n331 x 29 = 9599.
\n25 x 16 = 400.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe product 240 is equal to A.
\nthe product 100 is equal to B.
\nthe product 462 is equal to C.
\nthe product 255 is equal to D.
\nthe product 400 is equal to E.
\nproduct 9 is equal to F.
\nproduct 3 is equal to G.
\nproduct 9 is equal to H.
\n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-4-<\/p>\n

Topic 4 Vocabulary Review<\/strong><\/p>\n

Glossory<\/strong><\/p>\n

Word List<\/strong>
\n\u2022 compatible numbers
\n\u2022 estimate
\n\u2022 exponent
\n\u2022 overestimate
\n\u2022 partial products
\n\u2022 power of 10
\n\u2022 product
\n\u2022 underestimate<\/p>\n

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

Question 1.
\nMultiplying a decimal by 104 shifts the decimal point 4 places to the right.<\/p>\n

Answer:
\n104 x 2.1 = 218.4.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n104 x 2.1 = 218.4.
\nwe will use compatible numbers.<\/p>\n

Question 2.
\nThe product of a whole number and a decimal number is a whole number.<\/p>\n

Answer:
\nThe product of a whole number and a decimal number is a whole number.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nfor example:
\nif we divide the whole number by decimal number.
\nwe will get decimal numbers.
\nso the product of a whole number and a decimal number is a whole number.<\/p>\n

Question 3.
\nThe product of two decimal numbers less than 1 is greater than either factor.<\/p>\n

Answer:
\n0.1 x 0.2 = 0.02.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n0.1 x 0.2.
\n0.02.
\nthe two decimal numbers is less than 1.<\/p>\n

Question 4.
\nThe product of a number multiplied by 0.1 is 10 times as much as multiplying the same number by 0.01.<\/p>\n

Answer:
\n0.1 x 10 = 1.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe product of a number multiplied by 0.1.
\n0.1 x 10 = 1.
\nbut they have given the 0.01.
\nso the expression was wrong.<\/p>\n

Cross out the numbers that are NOT powers of 10.<\/p>\n

Question 5.
\n106<\/sup> 40 \u00d7 103<\/sup> 1 \u00d7 0.001 0.55 0.001<\/p>\n

Answer:
\nThe numbers that are not powers of 10 are 0.55 and 0.001.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 106<\/sup> 40 \u00d7 103<\/sup> 1 \u00d7 0.001 0.55 0.001.
\n0.55 and 0.001 are not the powers of 10.
\nso the numbers that are not powers of 10 are 0.55 and 0.001.<\/p>\n

Draw a line from each number in Column A to the same value in Column B. Column A<\/p>\n

\"Envision<\/p>\n

Answer:
\n7.2 x 1000 = 7.2 x 10 x 10 x 10.
\n0.38 x 10000 = 3800.
\n240 x 0.03 = 7.2.
\n3.8 x 0.1 = 0.38.
\n0.08 x 0.9 = 0.072.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers are 7.2 x 1000.
\n7.2 x 1000 = 7.2 x 10 x 10 x 10.
\n0.38 x 10000 = 3800.
\n240 x 0.03 = 7.2.
\n3.8 x 0.1 = 0.38.
\n0.08 x 0.9 = 0.072.
\n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-4-<\/p>\n

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

Question 11.
\nThe digits in the product of 0.48 and a decimal number between 350 and 400 are 182136. Explain how to correctly place the decimal point without knowing the other factor. Then place the decimal point in the product.<\/p>\n

Answer:
\nThe missing number is 379.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe digits in the product of 0.48 and a decimal number between 350 and 400 are 182136.
\n182136\/0.48 = 379.
\nso the number between 350 and 400 is 379.<\/p>\n

Topic 4 Reteaching<\/h3>\n

Set A<\/strong>
\npages 129-132, 133-136<\/p>\n

Use the patterns in this table to find 8.56 \u00d7 10 and 0.36 \u00d7 100.
\n\"Envision<\/p>\n

Remember<\/strong> you can use rounding or compatible numbers to estimate.<\/p>\n

Find each product.<\/p>\n

Question 1.
\n10 \u00d7 4.5<\/p>\n

Answer:
\n10 x 4.5 = 45.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 10 and 4.5.
\nmultiply the numbers.
\n10 x 4.5 = 45.<\/p>\n

Question 2.
\n103<\/sup> \u00d7 3.67<\/p>\n

Answer:
\n3.67 x 1000 = 3670.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 3.67 and 1000.
\nmultiply the numbers.
\n3.67 x 1000 = 3670.<\/p>\n

Question 3.
\n100 \u00d7 4.5<\/p>\n

Answer:
\n100 x 4.5 = 450.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 100 and 4.5.
\nmultiply the numbers.
\n100 x 4.5 = 450.<\/p>\n

Question 4.
\n0.008 \u00d7 102<\/sup><\/p>\n

Answer:
\n0.08 x 100 = 8.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 100 and 0.08.
\nmultiply the numbers.
\n0.08 x 100 = 8.<\/p>\n

Estimate each product.<\/p>\n

Question 5.
\n0.38 \u00d7 99<\/p>\n

Answer:
\n0.38 x 99 = 3.42.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 0.38 and 99.
\nmultiply the numbers.
\n0.38 x 99 = 3.42.<\/p>\n

Question 6.
\n8 \u00d7 56.7<\/p>\n

Answer:
\n8 x 56.7 = 453.6.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 8 and 56.7.
\nmultiply the numbers.
\n8 x 56.7 = 453.6.<\/p>\n

Question 7.
\n11 \u00d7 4.89<\/p>\n

Answer:
\n11 x 4.89 = 53.79.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 11 and 4.8.
\nmultiply the numbers.
\n11 x 4.89 = 53.79.<\/p>\n

Question 8.
\n24 \u00d7 3.9<\/p>\n

Answer:
\n24 x 3.9 = 93.6.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 24 and 3.9.
\nmultiply the numbers.
\n24 x 3.9 = 93.6.<\/p>\n

Set B<\/strong>
\npages 137-140, 141-144
\nFind 3 \u00d7 0.15.
\nModel the multiplication as repeated addition with place-value blocks.
\n\"Envision
\nSo, 3 \u00d7 0.15 = 0.45.<\/p>\n

Remember<\/strong> to estimate by rounding or using compatible numbers to check the reasonableness of the answer.<\/p>\n

Find each product. Use place-value blocks as necessary<\/p>\n

Question 1.
\n50 \u00d7 3.67<\/p>\n

Answer:
\n50 x 3.67 = 183.5.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 50 and 3.67.
\nmultiply the numbers.
\n50 x 3.67 = 183.5.<\/p>\n

Question 2.
\n5.86 \u00d7 5<\/p>\n

Answer:
\n5.86 x 5 = 29.3.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 5 and 5.86.
\nmultiply the numbers.
\n5.86 x 5 = 29.3.<\/p>\n

Question 3.
\n14 \u00d7 9.67<\/p>\n

Answer:
\n14 x 9.67 = 135.38.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 14 and 9.67.
\nmultiply the numbers.
\n14 x 9.67 = 135.38.<\/p>\n

Question 4.
\n8 \u00d7 56.7<\/p>\n

Answer:
\n8 x 56.7 = 453.6.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 8 and 56.7.
\nmultiply the numbers.
\n8 x 56.7 = 453.6.<\/p>\n

Question 5.
\n11 \u00d7 0.06<\/p>\n

Answer:
\n11 x 0.06 = 0.66.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 11 and 0.06.
\nmultiply the numbers.
\n11 x 0.06 = 0.66.<\/p>\n

Question 6.
\n2.03 \u00d7 6<\/p>\n

Answer:
\n2.03 x 6 = 12.18.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 2.03 and 6.
\nmultiply the numbers.
\n2.03 x 6 = 12.18.<\/p>\n

Question 7.
\n25 \u00d7 1.63<\/p>\n

Answer:
\n25 x 1.63 = 40.75.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 25 and 1.63.
\nmultiply the numbers.
\n25 x 1.63 = 40.75.<\/p>\n

Question 8.
\n5.62 \u00d7 75<\/p>\n

Answer:
\n5.62 x 75 = 421.5.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 5.62 and 75.
\nmultiply the numbers.
\n5.62 x 75 = 421.5.<\/p>\n

Set C<\/strong>
\npages 145-148, 149-152<\/p>\n

Find 0.2 \u00d7 1.7.
\nModel using hundredths grids.
\n\"Envision
\nThe product is where the shading overlaps. So, 0.2 \u00d7 1.7 = 0.34.<\/p>\n

Find each product.<\/p>\n

Question 1.
\n1.3 \u00d7 0.4<\/p>\n

Answer:
\nThe product is 0.52.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 1.3 and 0.4.
\nmultiply the numbers.
\n1.3 x 0.4 = 0.52.
\nso the product is 0.52.<\/p>\n

Question 2.
\n5.8 \u00d7 5.2<\/p>\n

Answer:
\nThe product is 30.16.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 5.8 and 5.2.
\nmultiply the numbers.
\n5.8 x 5.2 = 30.16.
\nso the product is 30.16.<\/p>\n

Question 3.
\n8.3 \u00d7 10.7<\/p>\n

Answer:
\nThe product is 30.16.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 5.8 and 5.2.
\nmultiply the numbers.
\n5.8 x 5.2 = 30.16.
\nso the product is 30.16.<\/p>\n

Question 4.
\n3.4 \u00d7 0.7<\/p>\n

Answer:
\nThe product is 2.38.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 3.4 and 0.7.
\nmultiply the numbers.
\n3.4 x 0.7 = 2.38.
\nso the product is 2.38.<\/p>\n

Question 5.
\n2.4 \u00d7 3.6<\/p>\n

Answer:
\nThe product is 8.64.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 2.4 and 3.6.
\nmultiply the numbers.
\n2.4 x 3.6 = 8.64.
\nso the product is 8.64.<\/p>\n

Question 6.
\n9.7 \u00d7 11.2<\/p>\n

Answer:
\nThe product is 108.64.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 9.7 and 11.2.
\nmultiply the numbers.
\n9.7 x 11.2 = 108.64.
\nso the product is 108.64.<\/p>\n

Question 7.
\n1.5 \u00d7 0.6<\/p>\n

Answer:
\nThe product is 0.9.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 1.5 and 0.6.
\nmultiply the numbers.
\n1.5 x 0.6 = 0.9.
\nso the product is 0.9.<\/p>\n

Question 8.
\n67.5 \u00d7 9.2<\/p>\n

Answer:
\nThe product is 621.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 67.5 and 9.2.
\nmultiply the numbers.
\n67.5 x 9.2 = 621.
\nso the product is 621.<\/p>\n

Set D<\/strong>
\npages 153-156 Use properties to find 0.8 \u00d7 0.4.<\/p>\n

Rewrite each decimal as a product of a whole number and a decimal. Next, use the Associative and Commutative Properties to rearrange the factors.
\n0.8 \u00d7 0.4 =
\n= (8 \u00d7 0.1) \u00d7 (4 \u00d7 0.1)
\n= (8 \u00d7 4) (0.1 \u00d7 0.1)
\n= 32 \u00d7 0.01
\n= 0.32
\nSo, 0.8 \u00d7 0.4 = 0.32<\/p>\n

Remember<\/strong> if two factors less than one are multiplied, their product is less than either factor.<\/p>\n

Use properties to find each product.<\/p>\n

Question 1.
\n0.6 \u00d7 0.3<\/p>\n

Answer:
\n0.6 x 0.3 = 18.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 0.6 and 0.3.
\n6 x 0.1 = 0.6.
\n3 x 0.1 = 0.7.
\n6 x 3 = 18.
\n18 x 0.1<\/p>\n

Question 2.
\n2.5 \u00d7 0.7<\/p>\n

Answer:
\n2.5 x 0.7 = 1.75.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 2.5 and 0.7.
\n25 x 0.1 = 2.5.
\n7 x 0.1 = 0.7.
\n25 x 7 x 0.01 = 1.75.<\/p>\n

Question 3.
\n0.04 \u00d7 1.9<\/p>\n

Answer:
\n0.04 x 1.9 = 0.076.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 0.04 and 1.9.
\n0.04 x 1.9 = 0.076.<\/p>\n

Question 4.
\n0.23 \u00d7 0.8<\/p>\n

Answer:
\n0.23 x 0.8 = 0.184.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n23 x 0.1 = 0.23.
\n8 x 0.1 = 0.8.
\n23 x 8 = 184.
\n0.1 x 0.1 = 0.01.
\n0.23 x 0.8 = 0.184.<\/p>\n

Question 5.
\n0.1 \u00d7 8.2<\/p>\n

Answer:
\n0.1 x 8.2 = 0.82.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n1 x 0.1 = 0.1.
\n82 x 0.1 = 0.82.
\n1 x 82 = 82.
\n0.1 x 0.1 = 0.01.
\n0.1 x 8.2 = 0.82.<\/p>\n

Question 6.
\n5.7 \u00d7 3.6<\/p>\n

Answer:
\n5.7 x 3.6 = 20.52.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n57 x 0.1 = 5.7.
\n36 x 0.1 = 3.6.
\n57 x 36 x 0.01 = 20.52.<\/p>\n

Question 7.
\n4.2 \u00d7 6.5<\/p>\n

Answer:
\n4.2 x 6.5 = 27.3.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n42 x 0.1 = 4.2.
\n65 x 0.1 = 6.5.
\n4.2 x 6.5 = 27.3.<\/p>\n

Question 8.
\n9.11 \u00d7 0.3<\/p>\n

Answer:
\n9.11 x 0.3 = 2.733.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n911 x 0.01 = 9.11.
\n3 x 0.1 = 0.3.
\n9.11 x 0.3 = 2.733.<\/p>\n

Set E<\/strong>
\npages 157-160
\nThe decimal is missing in the product below. Use number sense to place the decimal point correctly.
\n43.5 \u00d7 1.7 = 7395
\n\"Envision
\nSince 1.7 is greater than 1, the product will be greater than 43.5. Since 43.5 is about 40 and 1.7 is about 2, the answer will be about 80. The decimal point should be between the 3 and the 9.
\nSo, 43.5 \u00d7 1.7 = 73.95.<\/p>\n

Remember<\/strong> that it may be Reteaching helpful to compare each factor to 1 in order to determine the relative size of the product.<\/p>\n

The decimal point is missing in each product. Use number sense to place the decimal point correctly.<\/p>\n

Question 1.
\n4 \u00d7 0.21 = 84<\/p>\n

Answer:
\n4 x 0.21 = 0.84.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe two numbers are 4 and 0.21.
\nmultiply the numbers.
\n4 x 0.21 = 0.84.<\/p>\n

Question 2.
\n4.5 \u00d7 6.2 = 279
\nAnswer:<\/p>\n

Question 3.
\n7 \u00d7 21.6 = 1512
\nAnswer:<\/p>\n

Question 4.
\n6.4 \u00d7 3.2 = 2048
\nAnswer:<\/p>\n

Question 5.
\n31.5 \u00d7 0.01 = 315
\nAnswer:<\/p>\n

Question 6.
\n1.4 \u00d7 52.3 = 7322
\nAnswer:<\/p>\n

Question 7.
\n0.12 \u00d7 0.9 = 108
\nAnswer:<\/p>\n

Question 8.
\n12.5 \u00d7 163.2 = 2040
\nAnswer:<\/p>\n

Set F<\/strong>
\npages 161-164
\nThink about these questions to help you model with math.<\/p>\n

Thinking Habits<\/strong><\/p>\n

\u2022 How can I use math I know to help solve this problem?
\n\u2022 How can I use numbers, words, and symbols to solve the problem?
\n\u2022 How can I use pictures, objects, or an equation to represent the problem?
\n\"Envision<\/p>\n

Remember<\/strong> that you can write an equation to show how the quantities in a problem are related.
\nMr. Jennings made the stained glass window below with the dimensions shown. What is the total area of the window?<\/p>\n

Question 1.
\nWhat do you need to find first?
\nAnswer:<\/p>\n

Question 2.
\nWrite an equation to model the problem. Then solve the problem.
\nAnswer:<\/p>\n

Patti went to the bakery. She bought a loaf of bread for $3.49, 6 muffins that cost $1.25 each, and a bottle of juice for $1.79. She gave the cashier a $20 bill. How much change should Patti receive?<\/p>\n

Question 3.
\nWhat do you need to find first?<\/p>\n

Answer:
\nThe change should Patti receive = $13.47.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nPatti went to the bakery.
\nShe bought a loaf of bread for $3.49, 6 muffins that cost $1.25 each, and a bottle of juice for $1.79.
\nShe gave the cashier a $20 bill.
\n3.49 + 1.25 + 1.79 =
\n20 – 6.53 = 13.47.
\nso the change should patti receive = $13.47.<\/p>\n

Question 4.
\nAnswer the question. Write equations to show your work.<\/p>\n

Answer:
\nThe change should Patti receive = $13.47.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nPatti went to the bakery.
\nShe bought a loaf of bread for $3.49, 6 muffins that cost $1.25 each, and a bottle of juice for $1.79.
\nShe gave the cashier a $20 bill.
\n3.49 + 1.25 + 1.79 =
\n20 – 6.53 = 13.47.
\nso the change should patti receive = $13.47<\/p>\n

Topic 4 Assessment Practice<\/h3>\n

Question 1.
\nA credit card is 0.76 mm thick. How thick is a stack of 103 credit cards? Explain.<\/p>\n

Answer:
\nThe thick is a stack of 103 credit cards = 78.28 mm thick.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA credit card is 0.76 mm thick.
\n103 x 0.76 = 78.28.
\nso the thick is a stack of 78.28 mm.<\/p>\n

Question 2.
\nLeo has 59 bricks each measuring 0.19 m long. He lines up the bricks to make a row.
\nA. Estimate the length of Leo’s row of bricks. Write an equation to model your work.
\nB. Find the actual length of the row of bricks.<\/p>\n

Answer:
\nThe actual length of the row of bricks = 11.21 m.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nLeo has 59 bricks each measuring 0.19 m long.
\nHe lines up the bricks to make a row.
\n59 x 0.19 = 11.21 m.
\nso the actual length of the row of bricks = 11.21 m.<\/p>\n

Question 3.
\nSusan colored in the decimal grid shown below. Write an expression that shows the area she colored. Then evaluate the expression.
\n\"Envision<\/p>\n

Answer:
\nThe area she colored = 0.24.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nl = 0.8 and w = 0.3.
\n0.3 x 0.8 = 0.24.
\nso the area she colored = 0.24.<\/p>\n

Question 4.
\nMatch each expression on the left with its product.
\n\"Envision<\/p>\n

Answer:
\n5 x 0.08 = 0.4.
\n0.5 x 0.08 = 0.04.
\n50 x 0.8 = 40.
\n5 x 0.8 = 4.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nmatch each expression with its product.
\n5 x 0.08 = 0.4.
\n0.5 x 0.08 = 0.04.
\n50 x 0.8 = 40.
\n5 x 0.8 = 4.
\n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-4-<\/p>\n

Question 5.
\nMichelle bought 4.6 yards of fabric. Each yard of fabric cost $4.95. How much did Michelle spend on fabric? Enter your answer in the box.<\/p>\n

Answer:
\nThe Michelle spend on fabric = $22.77.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nMichelle bought 4.6 yards of fabric.
\nEach yard of fabric costs $4.95.
\n4.6 x $4.95 = 22.77.
\nso the Michelle spend on fabric = $22.77.<\/p>\n

Question 6.
\nChoose all the expressions that are equal to 0.75 \u00d7 0.5.
\n\"Envision<\/p>\n

Answer:
\nThe expressions are 5\/10 x 75\/100 and 75\/100 x 5\/10.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe expressions are 5\/10 x 75\/10, 5\/10 x 75\/100, 5\/100 x 75\/100, 50\/100 x 75\/100, and 75\/100 x 5\/10.
\n0.75 x 0.5 = 0.375.
\n5\/10 x 75\/10 = 0.5 x 7.5 = 3.75.
\n5\/10 x 75\/100 = 0.5 x 0.75 = 0.375.
\n5\/100 x 75\/100 = 0.05 x 0.75 = 0.0375.
\n50\/100 x 75\/100 = 0.75 x 0.05 = 0.0375.
\n75\/100 x 5\/10 = 0.75 x 0.5 = 0.375.<\/p>\n

Question 7.
\nSelect each equation that the number 102<\/sup> makes true.
\n\"Envision 0.031 \u00d7 \"Envision = 31
\n\"Envision 0.501 \u00d7 \"Envision = 501
\n\"Envision 04.08 \u00d7 \"Envision = 408
\n\"Envision 0.97 \u00d7 \"Envision = 97
\n\"Envision 55 \u00d7 \"Envision = 550<\/p>\n

Answer:
\n55 x 10 = 550.<\/p>\n

Explanation:
\nIn the above-given question that,
\ngiven that,
\n0.031 x 10 = 0.31.
\n0.501 x 10 = 5.01.
\n4.08 x 10 = 40.8.
\n0.97 x 10 = 9.7.
\n55 x 10 = 550.<\/p>\n

Question 8.
\nNadia drew a square in her notebook. Each side measured 2.5 centimeters.
\n\"Envision
\nA. What is the perimeter of Nadia’s square? Write an equation to model your work.
\nB. What is the area of Nadia’s square? Write an equation to model your work.<\/p>\n

Answer:
\nA. The perimeter of Nadia’s square = 10 cm.
\nB. the area of square = 6.25 sq cm.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe side of the square is 2.5 cm.
\nperimeter of square = 4 x side.
\n4 x 2.5 = 10 cm.
\narea of square = side x side.
\n2.5 x 2.5 = 6.25.
\nso the area of the square is 6.25 cm.<\/p>\n

Question 9.
\nMatch each expression on the left with its product.
\n\"Envision<\/p>\n

Answer:
\n3.04 x 100 = 304.
\n0.304 x 10000 = 3040.
\n3.04 x 10 = 30.4.
\n0.304 x 10 = 3.04.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nmatch each expression with its product.
\n3.04 x 100 = 304.
\n0.304 x 10000 = 3040.
\n3.04 x 10 = 30.4.
\n0.304 x 10 = 3.04.
\n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-4-<\/p>\n

Question 10.
\nSelect all the expressions that are equal to 0.09 \u00d7 0.4.
\n\"Envision<\/p>\n

Answer:
\nThat epressions are A and B.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n0.09 x 0.4 = 0.036.
\n9\/100 x 4\/10 = 0.09 x 0.4 = 0.036.
\n4\/10 x 9\/100 = 0.09 x 0.4 = 0.036.
\n4\/100 x 9\/100 = 0.9 x 0.4 = 0.36.
\n40\/100 x 9\/100 = 0.4 x 0.09 = 0.036.
\nso the expressions are true is A and B.<\/p>\n

Question 11.
\nOne glass of lemonade has 115 calories. How many calories are in 3.5 glasses of lemonade? Write an equation to model your work.<\/p>\n

Answer:
\nThe number of calories in 3.5 glasses of lemonade = 402.5.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nOne glass of lemonade has 115 calories.
\n3.5 x 115 = 402.5.
\nso the number of calories in 3.5 glasses of lemonade = 402.5.<\/p>\n

Question 12.
\nNatalie likes to mail lots of postcards when she goes on vacation. In 2014, the cost of a postcard stamp was $0.34.
\nA. Natalie buys 10 postcard stamps. What is the total cost of the stamps? Explain.
\nB. Natalie and her friends decide to buy 100 postcard stamps. What will be the total cost of the stamps? Explain.<\/p>\n

Answer:
\nA. The total cost of 10 postcard stamps = 3.4.
\nB. The total cost of 100 postcard stamps = 34.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nNatalie likes to mail lots of postcards when she goes on vacation.
\nIn 2014, the cost of a postcard stamp was $0.34.
\n10 x 0.34 = 3.4.
\n100 x 0.34 = 34.
\nso the total cost of 10 postcard stamps = 3.4.
\nThe total cost of 100 postcard stamps = 34.<\/p>\n

Question 13.
\nWithout doing the multiplication, match each expression on the left with the correct product. Use number sense to help you.
\n\"Envision<\/p>\n

Answer:
\n8.32 x 1.15 = 9.568.
\n5.78 x 0.35 = 2.023.
\n6.12 x 4.85 = 29.682.
\n7.95 x 2.48 = 19.716.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nmatch each expression with its product.
\n8.32 x 1.15 = 9.568.
\n5.78 x 0.35 = 2.023.
\n6.12 x 4.85 = 29.682.
\n7.95 x 2.48 = 19.716.
\n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-4-<\/p>\n

Question 14.
\nDerrick runs 2.25 miles each day. How many total miles will he have run after 10 days? Explain.<\/p>\n

Answer:
\nThe total number of miles will he have run after 10 days = 22.5 miles.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nDerrick runs 2.25 miles each day.
\n2.25 x 10 = 22.5 miles.
\nso the total number of miles will he have run after 10 days = 22.5 miles.<\/p>\n

Question 15.
\nSelect each equation that the decimal 0.65 makes true.
\n\"Envision 102<\/sup> \u00d7 \"Envision = 65
\n\"Envision 104<\/sup> \u00d7 \"Envision = 650
\n\"Envision 101<\/sup>\u00d7 \"Envision = 6.5
\n\"Envision 103<\/sup>\u00d7 \"Envision = 65
\n\"Envision 101<\/sup> \u00d7 \"Envision = 65<\/p>\n

Answer:
\nThe equation that are true is 100 x 0.65 = 65, 10 x 0.65 = 6.5.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n100 x 0.65 = 65.
\n10000 x 0.65 = 6500.
\n10 x 0.65 = 6.5.
\n1000 x 0.65 = 650.
\n10 x 0.65 = 6.5.<\/p>\n

Question 16.
\nA farmer plants 0.4 of a field with wheat. The field is 2.3 acres.
\nA. Shade the grids to model the multiplication.
\n\"Envision
\nB. How many acres are planted with wheat? Use an equation and the model to explain.<\/p>\n

Answer:
\nThe number of acres is planted with wheat = 5.75 acres.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA farmer plants 0.4 of a field with wheat.
\nThe field is 2.3 acres.
\n2.3 \/ 0.4 = 5.75.
\nso the number of acres is planted with wheat = 5.75 acres.<\/p>\n

Question 17.
\nBradley walks 0.65 mile each Friday to his friend’s house. He takes a different route home that is 1.2 miles. How many miles will Bradley walk to his friend’s house and back in a year? Show your work. Reminder: there are 52 weeks in a year.<\/p>\n

Answer:
\nThe number of miles will Bradley walk to his friend’s house and back in a year = 0.78 miles.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nBradley walks 0.65 miles each Friday to his friend’s house.
\nHe takes a different route home that is 1.2 miles.
\n0.65 x 1.2 = 0.78.
\nso the number of miles will Bradley walk to his friend’s house and back in a year = 0.78 miles.<\/p>\n

Question 18.
\nAlyssa paints 3 walls blue. Each of the walls is 8.3 feet tall and 7.5 feet wide.
\nA. Round the length and width to the nearest whole number. Then estimate the area that Alyssa will paint. Write equations to model your work.
\nB. Find the exact area. Write equations to model your work.
\nC. Compare your estimate to the exact answer. Why is your answer reasonable?<\/p>\n

Answer:
\nThe exact area = 47.4.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nAlyssa paints 3 walls blue. Each of the walls is 8.3 feet tall and 7.5 feet wide.
\n8.3 + 7.5 = 15.8.
\n15.8 x 3 = 47.4.
\nso the exact area is 47.4.<\/p>\n

Question 19.
\nLeticia and Jamal go to a bakery.
\n\"Envision
\nA. Jamal wants to buy 6 muffins. How much will this cost? Write an equation to model your work.
\nB. Leticia wants to buy 12 bagels. She uses partial products to find her total. She says “$16.80 is close to my estimate of 12 \u00d7 $1 = $12, so this total is reasonable.” Do you agree with her? Explain your reasoning
\n\"Envision<\/p>\n

Answer:
\nA. The cost of 6 muffins = $1.99.
\nB. No, it is not reasonable.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nLeticia and Jamal go to a bakery.
\nthe cost of the bagel is $0.95.
\nthe cost of the Muffin is $1.99.
\n1.99 x 6 = 11.94.
\n0.95 x 12 = 11.4.<\/p>\n

Question 20.
\nThe area of one fabric square is 4.85 square inches. What is the area of a quilt made with 102<\/sup> fabric squares? Explain.<\/p>\n

Answer:
\nThe area of the quilt made with 100 fabric squares = 485 in.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe area of one fabric square is 4.85 square inches.
\n4.85 x 100 = 485.
\nso the area of the quilt made with 100 fabric squares = 485 sq in.<\/p>\n

Question 21.
\nJen bought 3.72 pounds of apples at a farmer’s market. Andrea bought 4 times as much as Jen.
\n\"Envision
\nA. Which expression represents the problem? Use the bar diagram to help.
\nA. 3.72 \u00d7 4
\nB. 3.72 \u00d7 1
\nC. 3.72 \u00f7 4.
\nD. 3.72 \u00f7 1<\/p>\n

Answer:
\nOption C is the correct answer.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJen bought 3.72 pounds of apples at a farmer’s market.
\nAndrea bought 4 times as much as Jen.
\n3.72 \/ 4 = 0.93.
\nso option C is the correct answer.<\/p>\n

B. How many pounds of apples did Andrea buy?<\/p>\n

Answer:
\nThe number of pounds of apples did Andrea buy = 0.93 pounds.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJen bought 3.72 pounds of apples at a farmer’s market.
\nAndrea bought 4 times as much as Jen.
\n3.72 \/ 4 = 0.93.
\nso the number of pounds of apples did Andrea buy = 0.93.<\/p>\n

Topic 4 Performance Task<\/h3>\n

An exchange rate is how much of one country’s currency (money) you would get for another country’s currency. The table below shows the recent exchange rate between the U.S. dollar and the currency of some other countries.
\nFor example, if you had $2 (U.S.) dollars, you could exchange that for 26.48 Mexican pesos:
\n2 \u00d7 13.24 = 26.48.
\n\"Envision<\/p>\n

Question 1.
\nJade has $10, Julio has $100, and Anna has $1,000. How many Japanese yen would each person get in exchange for their dollars?<\/p>\n

Answer:
\nThe Japanese yen would each person get in exchange for their dollars = $1.0182.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJade has $10, Julio has $100, and Anna has $1,000.
\nJapanese yen has 101.82.
\n101.82\/10 = 10.182.
\n101.82\/100 = 1.0182.
\n101.82\/1000 = 0.10182.<\/p>\n

Question 2.
\nIvana has $5.50. Luc has 1.4 times as much money as Ivana.<\/p>\n

Part A<\/strong>
\nHow many Indian rupees would Ivana get?
\nPart B<\/strong>
\nHow many dollars does Luc have? How many rupees can he exchange for that? Round your answer to the nearest hundredth.<\/p>\n

Answer:
\nThe number of rupees can he exchange for that = $3.92.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nIvana has $5.50. Luc has 1.4 times as much money as Ivana.
\n5.50\/1.4 = 3.92.
\nso the number of rupees can he exchange for that = $3.92.<\/p>\n

Question 3.
\nUse estimation to solve. Marcus has $250. About how many Venezuelan bol\u00edvares could he obtain? Is your estimate an overestimate or an underestimate? Explain.<\/p>\n

Answer:
\nThe number of Venezuelan bolivares could he obtain = $38.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nMarcus has $250.
\n250\/6.59 = 37.9.
\nso the number of Venezuelan bolivares could he obtain = $37.9.<\/p>\n

Question 4.
\nJorge is traveling to Kenya to photograph wildlife. How many Kenyan shillings will he receive for $500? His friends give him a $50 gift certificate right before he leaves. How many Kenyan shillings can he exchange for that amount?<\/p>\n

Answer:
\nThe Kenyan shillings can be exchanged for that amount = 10.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJorge is traveling to Kenya to photograph wildlife.
\nHis friends give him a $50 gift certificate right before he leaves.
\n500\/50 = 10.
\nso the Kenyan shillings can be exchanged for that amount = 10.<\/p>\n

Question 5.
\nKofi is taking a trip to Mexico to see Mayan and Aztec pyramids. He wants to exchange $300 before arriving there. How many Mexican pesos can he receive? Write and solve an equation to show your work.<\/p>\n

Answer:
\nThe number of Mexican pesos can he receive = 0.044 pesos.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nKofi is taking a trip to Mexico to see the Mayan and Aztec pyramids.
\nHe wants to exchange $300 before arriving there.
\n13.24\/300 = 0.044.
\nso the number of Mexican pesos can he receive = 0.044.<\/p>\n

Question 6.
\nMary is planning a vacation to Europe. The exchange rate for the U.S. dollar to the Euro is 0.73.
\nPart A<\/strong>
\nSketch place-value blocks to model how many Euros Mary will get for 3 U.S. dollars.
\nPart B<\/strong>
\nHow many Euros can Mary get for $3? Write an equation to show your work.
\nPart C<\/strong>
\nHow does the model help you find the product?<\/p>\n

Answer:
\nThe number of Euros can Mary get for $3 = $0.24.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nMary is planning a vacation to Europe.
\nThe exchange rate for the U.S. dollar to the Euro is 0.73.
\n0.73\/3 = 0.24.
\nso the number of Euros can Mary get for $3 = $0.24<\/p>\n","protected":false},"excerpt":{"rendered":"

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