{"id":9388,"date":"2023-12-28T14:11:15","date_gmt":"2023-12-28T08:41:15","guid":{"rendered":"https:\/\/envisionmathanswerkey.com\/?p=9388"},"modified":"2023-12-29T12:12:27","modified_gmt":"2023-12-29T06:42:27","slug":"envision-math-common-core-grade-5-answer-key-topic-2","status":"publish","type":"post","link":"https:\/\/envisionmathanswerkey.com\/envision-math-common-core-grade-5-answer-key-topic-2\/","title":{"rendered":"enVision Math Common Core Grade 5 Answer Key Topic 2 Use Models and Strategies to Add and Subtract Decimals"},"content":{"rendered":"

Go through the\u00a0enVision Math Common Core Grade 5 Answer Key<\/a>\u00a0Topic 2 Use Models and Strategies to Add and Subtract Decimals<\/strong>\u00a0regularly and improve your accuracy in solving questions.<\/p>\n

enVision Math Common Core 5th Grade Answers Key Topic 2 Use Models and Strategies to Add and Subtract Decimals<\/h2>\n

Use Models and Strategies to Add and Subtract Decimals<\/strong><\/p>\n

Essential Questions:<\/strong> How can sums and differences of decimals be estimated? What are some common procedures for adding and subtracting decimals? How can sums and differences be found mentally?<\/p>\n

\"Envision
\nenVision STEM Project: Producers and Consumers<\/strong>
\nDo Research<\/strong> Use the Internet or other sources to find information about producers and consumers.
\nJournal: Write a Report<\/strong> Include what you found. Also in your report:<\/p>\n

    \n
  • What do producers need to survive? What do consumers need to survive?<\/li>\n
  • Give at least three examples of both producers and consumers.<\/li>\n
  • Write and solve decimal addition and subtraction problems for the amounts of food the consumers need.<\/li>\n<\/ul>\n

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

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

    Choose the best term from the box. Write it on the blank.<\/p>\n

    \u2022 addend
    \n\u2022 inverse operations
    \n\u2022 round
    \n\u2022 difference
    \n\u2022 equivalent
    \n\u2022 sum<\/p>\n

    Question 1.
    \nThe ___ is the result of subtracting one number from another.<\/p>\n

    Answer:
    \nThe difference is the result of subtracting one number from another.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe difference is the result of subtracting one number from another.
    \nfor example:
    \n5 – 2 = 3.
    \n3 is the difference.<\/p>\n

    Question 2.
    \nTwo numbers or expressions that have the same value are ___.<\/p>\n

    Answer:
    \nThe two numbers or expressions that have the same value are equivalent.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers or expressions that have the same value are equivalent.
    \nfor example:
    \n2 + 3 = 5.
    \nthe two have the same value.<\/p>\n

    \"Use<\/p>\n

    Question 3.
    \nThe answer to an addition problem is the ___.<\/p>\n

    Answer:
    \nThe answer to an addition problem is the sum.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe answer to an addition problem is the sum.
    \nfor example:
    \n5 + 3 = 8.
    \n8 is the sum.<\/p>\n

    Question 4.
    \nOne way to estimate an answer is to ___ the numbers and then do the calculation.<\/p>\n

    Answer:
    \nOne way to estimate an answer is to inverse the numbers and then do the calculation.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nOne way to estimate an answer is to inverse the numbers and then do the calculation.
    \n5 + 6 = 11.
    \n11 – 6 = 5.
    \n11 – 5 = 6.<\/p>\n

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

    Question 5.
    \n74.362<\/p>\n

    Answer:
    \nThe number equal to the nearest tenth = 74.4.<\/p>\n

    Explanation:
    \nIn the above-given that,
    \ngiven that,
    \nto round a number to the nearest tenth,
    \nlook at the next place value to the right(the hundredths).
    \nif it’s 4 or less, just remove all the digits to the right.
    \nif it’s 5 or greater, add 1 to the digit in the tenths place, and remove all the digits to the right.
    \n74.362 in this the hundredths place is greater than 5.
    \nso add 1 to the tenths place.
    \n3 + 1 = 4.
    \nthe number equal to the nearest tenth = 74.4.<\/p>\n

    Question 6.
    \n28.45<\/p>\n

    Answer:
    \nThe number equal to the nearest tenth = 28.5.<\/p>\n

    Explanation:
    \nIn the above-given that,
    \ngiven that,
    \nto round a number to the nearest tenth,
    \nlook at the next place value to the right(the hundredths).
    \nif it’s 4 or less, just remove all the digits to the right.
    \nif it’s 5 or greater, add 1 to the digit in the tenths place, and remove all the digits to the right.
    \n28.45 in this the hundredths place is greater than 5.
    \nso add 1 to the tenths place.
    \n4 + 1 = 5.
    \nthe number equal to the nearest tenth = 28.5.<\/p>\n

    Question 7.
    \n13.09<\/p>\n

    Answer:
    \nThe number equal to the nearest tenth = 13.1.<\/p>\n

    Explanation:
    \nIn the above-given that,
    \ngiven that,
    \nto round a number to the nearest tenth,
    \nlook at the next place value to the right(the hundredths).
    \nif it’s 4 or less, just remove all the digits to the right.
    \nif it’s 5 or greater, add 1 to the digit in the tenths place, and remove all the digits to the right.
    \n13.09 in this the hundredths place is greater than 5.
    \nso add 1 to the tenths place.
    \n0 + 1 = 1.
    \nthe number equal to the nearest tenth = 13.1.<\/p>\n

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

    Question 8.
    \n43.017<\/p>\n

    Answer:
    \nThe number equal to the nearest hundredth = 43.02.<\/p>\n

    Explanation:
    \nIn the above-given that,
    \ngiven that,
    \nto round a number to the nearest hundredth,
    \nlook at the next place value to the right(the thousands).
    \nif it’s 4 or less, just remove all the digits to the right.
    \nif it’s 5 or greater, add 1 to the digit in the hundreds place, and remove all the digits to the right.
    \n43.017 in this the thousands place is greater than 5.
    \nso add 1 to the hundredths place.
    \n1 + 1 = 2.
    \nthe number equal to the nearest hundredths = 43.02.<\/p>\n

    Question 9.
    \n186.555<\/p>\n

    Answer:
    \nThe number equal to the nearest hundredth = 186.56.<\/p>\n

    Explanation:
    \nIn the above-given that,
    \ngiven that,
    \nto round a number to the nearest hundredth,
    \nlook at the next place value to the right(the thousands).
    \nif it’s 4 or less, just remove all the digits to the right.
    \nif it’s 5 or greater, add 1 to the digit in the hundreds place, and remove all the digits to the right.
    \n186.555 in this the thousands place is greater than 5.
    \nso add 1 to the hundredths place.
    \n5 + 1 = 6.
    \nthe number equal to the nearest hundredths = 186.56.<\/p>\n

    Question 10.
    \n222.222<\/p>\n

    Answer:
    \nThe number equal to the nearest hundredth = 222.20.<\/p>\n

    Explanation:
    \nIn the above-given that,
    \ngiven that,
    \nto round a number to the nearest hundredth,
    \nlook at the next place value to the right(the thousands).
    \nif it’s 4 or less, just remove all the digits to the right.
    \nif it’s 5 or greater, add 1 to the digit in the hundreds place, and remove all the digits to the right.
    \n222.222 in this the thousands place is less than 5.
    \nso do not add 1 to the hundredths place.
    \n222.20
    \nthe number equal to the nearest hundredths = 222.20.<\/p>\n

    Round each number to the underlined digit.<\/p>\n

    Question 11.
    \n84<\/u>.59<\/p>\n

    Answer:
    \nThe number round to the underlined digit is = 85.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe number is 84.59.
    \nthe underlined digit is 4.
    \n4 + 1 = 5.
    \nso the number round to the underlined digit = 85.<\/p>\n

    Question 12.
    \n2.94<\/u>8<\/p>\n

    Answer:
    \nThe number round to the underlined digit is = 2.95.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe number is 2.948.
    \nthe underlined digit is 4.
    \n4 + 1 = 5.
    \nso the number round to the underlined digit = 2.95.<\/p>\n

    Question 13.
    \n30.12<\/u>5<\/p>\n

    Answer:
    \nThe number round to the underlined digit is = 30.13.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe number is 30.125.
    \nthe underlined digit is 2.
    \n2 + 1 = 3.
    \nso the number round to the underlined digit = 30.13<\/p>\n

    \"Use<\/p>\n

    Addition and Subtraction of Whole Numbers<\/strong><\/p>\n

    Find each sum or difference.<\/p>\n

    Question 14.
    \n9,536 + 495<\/p>\n

    Answer:
    \n9536 + 495 = 10031.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe numbers are 9536 and 495.
    \nadd the two numbers.
    \n9536 + 495 = 10031.<\/p>\n

    Question 15.
    \n612 – 357<\/p>\n

    Answer:
    \n612 – 357 = 255.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe numbers are 612 and 357.
    \nsubtract the two numbers.
    \n612 – 357 = 255.<\/p>\n

    Question 16.
    \n5,052 – 761<\/p>\n

    Answer:
    \n5052 – 761 = 4291.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe numbers are 5052 and 761.
    \nsubtract the two numbers.
    \n5052 – 761 = 4291.<\/p>\n

    Question 17.
    \nVivica sees that a printer costs $679 and a computer costs $1,358. What is the total cost of the printer and the computer?<\/p>\n

    Answer:
    \nThe total cost of the printer and the computer = $2037.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nVivica sees that a printer costs $679.
    \ncomputer costs $1,358.
    \n$679 + $1,358 = $2037.
    \nso the total cost of the printer and the computer = $2037.<\/p>\n

    Question 18.
    \nThe Pecos River is 926 miles long, and the Brazos River is 1,280 miles long. How many miles longer is the Brazos River than the Pecos River?
    \nA. 2,206 miles
    \nB. 1,206 miles
    \nC. 364 miles
    \nD. 354 miles<\/p>\n

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

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe Pecos River is 926 miles long, and the Brazos River is 1,280 miles long.
    \n1280 – 926 = 354.
    \nthe longer is the Brazos River than the Pecos River is 354 miles.
    \nso option D is correct.<\/p>\n

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

    PROJECT 2A<\/strong>
    \nHow big are alligators and crocodiles?
    \nProject: Compare the Sizes of Reptiles
    \n\"Envision<\/p>\n

    Answer:
    \nThe crocodile weight is 410 – 520 kg approximately.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe water animals are crocodiles and alligators.
    \nthe size of the reptiles is very tiny.
    \nso the crocodile weight is 410 – 520 kg approximately.<\/p>\n

    PROJECT 2B<\/strong>
    \nHow much should a theme park ticket cost?
    \nProject: Make a Brochure for a Theme Park
    \n\"Envision<\/p>\n

    Answer:
    \nThe cost of the ticket is $37 approximately.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe theme park is located in the united states of America.
    \nso the cost of the ticket is $37 approximately.<\/p>\n

    \"Use<\/p>\n

    PROJECT 2C<\/strong>
    \nHow much and how healthy is your meal in a restaurant?
    \nProject: Plan Your Meal
    \n\"Envision<\/p>\n

    PROJECT 2D<\/strong>
    \nHow far was your trip?
    \nProject: Make a Travel Journal
    \n\"Envision<\/p>\n

    Answer:
    \nThe travel trip is Vizag.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nmy travel trip is Vizag.
    \nthe distance from Hyderabad to Vizag is around 650 km.
    \nso my travel trip is Vizag.<\/p>\n

    Lesson 2.1 Mental Math<\/h3>\n

    Activity<\/strong>
    \nSolve & Share<\/strong><\/p>\n

    Three pieces of software cost $20.75, $10.59, and $18.25. What is the total cost of the software? Use mental math to solve.<\/p>\n

    You can use reasoning to help you. What do you know about adding three numbers that will make it easier to solve this problem?
    \n\"Envision<\/p>\n

    Answer:
    \nThe total cost of the software is $49.59.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThree pieces of software cost $20.75, $10.59, and $18.25.
    \n20.75 + 10.59 + 18.25 = 49.59.
    \nso the total cost of the software is $49.59.<\/p>\n

    Look Back!<\/strong> Which two numbers above were easy to add in your head? Why?<\/p>\n

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

    Essential Question<\/strong>
    \nHow Can You Use Mental Math to Add?<\/p>\n

    A.<\/strong>
    \nProperties of addition can help you find the total cost of these three items.<\/p>\n

    The Commutative Property and Associative Property make it easy to add $11.45 + $3.39 + $9.55.
    \n\"Envision<\/p>\n

    The Associative Property lets you change the grouping of addends.
    \n($11.45 + $3.39) + $9.55 = $11.45 + ($3.39 + $9.55)
    \n\"Envision
    \nThe Commutative Property lets you add two decimals in any order.<\/p>\n

    B.<\/strong>
    \nUse the Commutative Property to change the order.
    \n$11.45 + ($3.39 + $9.55) = $11.45 + ($9.55 + $3.39)
    \nUse the Associative Property to change the grouping.
    \n$11.45 + ($9.55 + $3.39) = ($11.45 + $9.55) + $3.39<\/p>\n

    C.<\/strong>
    \nAdd $11.45 and $9.55 first because they are easy to compute mentally.
    \n$11.45 + $9.55 = $21
    \n$21 + $3.39 = $24.39
    \nThe three items cost a total of $24.39.
    \nCompatible numbers are numbers that are easy to compute mentally.
    \n\"Envision<\/p>\n

    Convince Me!<\/strong> Reasoning Use mental math to find the sum. Explain your thinking. Jim earns $22.50, $14.75, and $8.50 on three different days. How much did he earn in all?<\/p>\n

    Answer:
    \nThe much did he earn in all = $45.75.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nJim earns $22.50, $14.75, and $8.50 on three different days.
    \nwe can find the answer in three ways.
    \n$22.50 + $14.75 = 37.25.
    \n$37.25 + $8.50 = $45.75.
    \nso the much did he earn in all = $45.75.<\/p>\n

    Another Example<\/strong>
    \nWith compensation, adjust one or both numbers to make the calculation easier. Then adjust the difference or sum to get the final answer.
    \nUse compensation to subtract.<\/p>\n

    Find 4.25 \u2013 0.08 mentally.
    \n4.25 \u2013 0.10 = 4.15
    \n\"Envision
    \n4.25 – 0.08 = 4.17<\/p>\n

    Use compensation to add.
    \nFind $3.47 + $4.35 mentally.
    \n\"Envision
    \n$3.47 + $4.35 = $7.82<\/p>\n

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

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

    Question 1.
    \nShow how to use compensation to add $3.18 and $6.50.<\/p>\n

    Answer:
    \n$3.18 + $6.50 = $9.68.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 3.20 and 6.50.
    \n$3.20 + $6.50 = $9.70.
    \nwe have to take 0.02 from $9.70.
    \n$9.70 – 0.02 = $9.68.
    \nso $3.18 + $6.50 = $9.68.<\/p>\n

    Question 2.
    \nUse properties to rewrite the expression to be easier to solve. Explain. (13 + 4.63) + 7.4<\/p>\n

    Answer:
    \nWe can use two expressions that are associative and commutative properties.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two properties are associative and commutative.
    \n13 + 4.63 = 17.63.
    \n17.63 + 7.4 = 25.03.
    \n4.63 + 7.4 = 12.03.
    \n12.03 + 13 = 25.03.
    \nso we can use two expressions that are associative and commutative properties.<\/p>\n

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

    In 3-6, use mental math to add or subtract.<\/p>\n

    Question 3.
    \n12 + 3.04 + 8.28<\/p>\n

    Answer:
    \n12 + 3.04 + 8.28 = 23.32.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nuse mental math to add.
    \n12 + 3.04 = 15.04.
    \n15.04 + 8.28 = 23.32.<\/p>\n

    \"Use<\/p>\n

    Question 4.
    \n6.97 + 4.15<\/p>\n

    Answer:
    \n6.97 + 4.15 = 11.12.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nuse mental math to add.
    \n6.97 + 4.15 = 11.12.<\/p>\n

    Question 5.
    \n9.04 \u2013 6.98<\/p>\n

    Answer:
    \n9.04 – 6.98 = 2.06.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nuse mental math to subtract.
    \n9.04 – 6.98 = 2.06.<\/p>\n

    Question 6.
    \n4.02 +0.19 + 16.48<\/p>\n

    Answer:
    \n4.02 + 0.19 + 16.48 = 20.69.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nuse mental math to add.
    \n4.02 + 0.19 = 4.21.
    \n4.21 + 16.48 = 20.69.<\/p>\n

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

    Leveled Practice In 7-12, use mental math to add or subtract.<\/p>\n

    Question 7.
    \n7.1 + 5.4 + 2.9 =
    \n___ + 5.4 =
    \n_______<\/p>\n

    Answer:
    \n7.1 + 5.4 + 2.9 = 15.4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nuse mental math to add.
    \n7.1 + 5.4 = 12.5.
    \n12.5 + 2.9 = 15.4.<\/p>\n

    Question 8.
    \n373.4 \u2013 152.9 =
    \n373.4 – __ = 220.4
    \n___ + 0.1 = ___<\/p>\n

    Answer:
    \n373.4 – 152.9 = 220.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nuse mental math to subtract.
    \n373.4 – 152.9 = 220.5.
    \n373.4 – 152.8 = 220.4.
    \n220.4 + 0.1 = 220.5.<\/p>\n

    Question 9.
    \n$18.25 + $7.99 + $4.75<\/p>\n

    Answer:
    \n$18.25 + $7.99 + $4.75 = $30.99.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nuse mental math to add.
    \n18.25 + 7.99 = 26.24.
    \n26.24 + 4.75 = 30.99.<\/p>\n

    Question 10.
    \n1.05 + 3 + 4.28 +0.95<\/p>\n

    Answer:
    \n1.05 + 3 + 4.28 + 0.95 = 6.31.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nuse mental math to add.
    \n1.05 + 3 = 1.08.
    \n4.28 + 0.95 = 5.23.
    \n5.23 + 1.08 = 6.31.<\/p>\n

    Question 11.
    \n2,504 + 140 + 160<\/p>\n

    Answer:
    \n2504 + 140 + 160 = 2804.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nuse mental math to add.
    \n2504 + 140 = 2644.
    \n2644 + 160 = 2804.<\/p>\n

    Question 12.
    \n35.7 \u2013 14.8<\/p>\n

    Answer:
    \n35.7 – 14.8 =20.9.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 35.7 and 14.8.
    \nuse mental math to subtract.
    \n35.7 – 14.8 = 20.9.<\/p>\n

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

    Question 13.
    \nJoanne bought three books that cost $3.95, $4.99, and $6.05. How much did she spend in all? Use compensation and mental math to find the sum.
    \n\"Envision<\/p>\n

    Answer:
    \nThe total she spends in all = 14.09.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nJoanne bought three books that cost $3.95, $4.99, and $6.05.
    \n$3.95 + $4.100 = 8.05.
    \n8.05 – 0.01 = 8.04.
    \n8.04 + 6.05 = 14.09.
    \nso the total she spends in all = 14.09.<\/p>\n

    Question 14.
    \nConstruct Arguments<\/strong> Use compensation to find each difference mentally. Explain how you found each difference.
    \nA. 67.9 – 29.9
    \nB. 456 – 198<\/p>\n

    Answer:
    \nA. 67.9 – 29.9 = 38.
    \nB. 456 – 198 = 258.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n67.9 + 0.01 = 68.0.
    \n68.0 – 0.01 = 67.9.
    \n67.9 – 29.9 = 38.
    \n456 – 200 = 256.
    \n256 + 2 = 258.<\/p>\n

    Question 15.
    \nNumber Sense<\/strong> The table shows how many points Eduardo scored during each game. Use mental math to find how many points he scored in the first three games.
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of points Eduardo scored in the first three games = 99.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe table shows how many points Eduardo scored during each game.
    \nin the first game, he scored 54 points.
    \nin the second game, he scored 19 points.
    \nin the third game, he scored 26 points.
    \n54 + 19 + 26 = 99.
    \nso the number of points Eduardo scored in the first three games = 99.<\/p>\n

    Question 16.
    \nOn three different days at her job, Sue earned $27, $33, and $49. She needs to earn $100 to buy a desk for her computer. If she buys the desk, how much money will she have left over?<\/p>\n

    Answer:
    \nThe money will she have leftover = 9.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nOn three different days at her job.
    \nSue earned $27, $33, and $49.
    \nShe needs to earn $100 to buy a desk for her computer.
    \n$27 + $33 + $49 = 109.
    \n109 – 100 = 9.
    \nso the money will she have leftover = 9.<\/p>\n

    Question 17.
    \nA shelf can hold 50 DVDs. Jill has 27 DVDs. She plans to buy 5 new ones. Each DVD costs $9. After she buys the new ones, how many more DVDs can the shelf hold?<\/p>\n

    Answer:
    \nThe number of DVDs can the shelf hold = 32.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA shelf can hold 50 DVDs. Jill has 27 DVDs.
    \nShe plans to buy 5 new ones.
    \nEach DVD costs $9.
    \n27 + 5 = 32.
    \nso the number of DVDs can the shelf hold = 32.<\/p>\n

    Question 18.
    \nWhen finding the difference of two numbers mentally, can you use the Commutative Property? Explain.<\/p>\n

    Answer:
    \nNo, we cannot use the commutative property.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe difference between the two numbers we cannot use the commutative property.
    \nfor example:
    \nthe two numbers are 5 and 3.
    \n5 – 3 = 2.
    \nso the difference is 2.<\/p>\n

    Question 19.
    \nHigher Order Thinking<\/strong> Daria bought a skein of alpaca yarn for $47.50, a skein of angora yarn for $32.14, a skein of wool yarn for $16.50, and a pair of knitting needles for $3.86. How much did she spend in all? Describe how you calculated your answer.<\/p>\n

    Answer:
    \nThe more did she spend in all = $100.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nDaria bought a skein of alpaca yarn for $47.50, a skein of angora yarn for $32.14.
    \na skein of wool yarn for $16.50, and a pair of knitting needles for $3.86.
    \n47.50 + 32.14 + 16.50 + 3.86.
    \n47.50 + 32.14 = 79.64.
    \n16.50 + 3.86 = 20.36.
    \n79.64 + 20.36 =
    \nso the more did she spend in all = $100.<\/p>\n

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

    Question 20.
    \nMrs. Healer’s class took a field trip to a park 12.3 miles away. Mr. Dean’s class drove 4.9 miles to the public library. How much farther did Mrs. Healer’s class travel than Mr. Dean’s class? Explain how you used mental math to determine the difference.<\/p>\n

    Answer:
    \nThe much farther did Mrs. Healer’s class travel than Mr. Dean’s class = 7.4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nMrs. Healer’s class took a field trip to a park 12.3 miles away.
    \nMr. Dean’s class drove 4.9 miles to the public library.
    \n12.3 – 4.9 = 7.4.
    \nso much farther did Mrs. Healer’s class travel than Mr.Dean’s class = 7.4.<\/p>\n

    Lesson 2.2 Estimate Sums and Differences of Decimals<\/h3>\n

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

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

    An amusement park has two roller coasters. One is 628 feet long, and the other is 485 feet long. If you ride both roller coasters, about how many feet will you travel in all? Use estimation to solve.<\/p>\n

    You can use reasoning to decide what you are asked to find. Is the problem looking for an exact answer? How can you tell?
    \n\"Envision<\/p>\n

    Look Back!<\/strong> About how much longer is the one coaster than the other? Show your work.<\/p>\n

    Answer:
    \nThe number of feet will you travel in all = 143 feet.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAn amusement park has two roller coasters.
    \nOne is 628 feet long, and the other is 485 feet long.
    \n628 – 485 = 143.
    \nso the number of feet will you travel in all = 143 feet.<\/p>\n

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

    Essential Question<\/strong> How Can You Estimate Sums?<\/p>\n

    A.<\/strong>
    \nStudents are collecting dog food to give to an animal shelter. Estimate how many pounds were collected in Weeks 3 and 4.
    \n\"Envision<\/p>\n

    There is more than one way to find an estimate.
    \n\"Envision<\/p>\n

    B. One Way<\/strong>
    \nRound each addend to the nearest hundred.
    \n\"Envision
    \n237.5 + 345.1 is about 500.
    \nThe students collected about 500 pounds of dog food in Weeks 3 and 4.<\/p>\n

    C.<\/strong>
    \nAnother Way<\/strong><\/p>\n

    Substitute compatible numbers.
    \n\"Envision
    \nCompatible numbers are easy to add!
    \n\"Envision
    \n237.5 + 345.1 is about 600.
    \nThe students collected about 600 pounds of dog food in Weeks 3 and 4.<\/p>\n

    Convince Me!<\/strong> Critique Reasoning Tom\u00e1s said, “We did great in Week 4! We collected just about twice as many pounds as in Week 1!”
    \nUse estimation to decide if he is right. Explain your thinking.<\/p>\n

    Another Example<\/strong>
    \nYou can estimate differences.
    \nEstimate 22.84 \u2013 13.97.<\/p>\n

    One Way<\/strong>
    \nRound each number to the nearest whole number.
    \n\"Envision
    \n22.84 \u2013 13.97 is about 9.<\/p>\n

    Another Way<\/strong>
    \nSubstitute compatible numbers.
    \n\"Envision
    \n22.84 \u2013 13.97 is about 10.<\/p>\n

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

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

    Question 1.
    \nIn the example above, which estimate is closer to the actual difference? How can you tell without subtracting?<\/p>\n

    Answer:
    \n22.84 is near to the 23.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nfor example:
    \n22.84 we can write it as 23.
    \n22.84 we can write it as 25.
    \nso 23 is near to 22.84.<\/p>\n

    Question 2.
    \nIn the example on the previous page, students collected more pounds of dog food in Week 4 than in Week 3. Estimate about how many more.<\/p>\n

    Answer:
    \nThe many more they have collected = 100 pounds.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 237.5 and 345.1.
    \n250 + 350 = 600.
    \nso the many more they have collected = 100 pounds.<\/p>\n

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

    In 3-10, estimate each sum or difference.<\/p>\n

    Question 3.
    \n49 + 22.88<\/p>\n

    Answer:
    \n49 + 23 = 72.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 49 and 23.
    \nadd the two numbers.
    \n49 + 23 = 72.<\/p>\n

    Question 4.
    \n86.9 \u2013 18<\/p>\n

    Answer:
    \n86.9 – 18 = 68.9<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 86.9 and 18.
    \nsubtract the two numbers.
    \n86.9 – 18 = 68.9.<\/p>\n

    Question 5.
    \n179 + 277.1<\/p>\n

    Answer:
    \n179 + 277.1 = 456.1<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 179 and 277.1.
    \nadd the two numbers.
    \n179 + 277.1 = 456.1.<\/p>\n

    Question 6.
    \n23.2 \u2013 9.71<\/p>\n

    Answer:
    \n23.2 – 9.71 =13.49<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 23.2 and 9.71.
    \nsubtract the two numbers.
    \n23.2 – 9.71 = 13.49.<\/p>\n

    Question 7.
    \n23.8 \u2013 4.7<\/p>\n

    Answer:
    \n23.8 – 4.7 = 19.1.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 23.8 and 4.7.
    \nsubtract the two numbers.
    \n23.8 – 4.7 = 19.1.<\/p>\n

    Question 8.
    \n87.2 + 3.9<\/p>\n

    Answer:
    \n87.2 + 3.9 = 91.1.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 87.2 and 3.9.
    \nadd the two numbers.
    \n87.2 – 3.9 = 91.1.<\/p>\n

    Question 9.
    \n38.9 – 21.4<\/p>\n

    Answer:
    \n38.9 – 21.4 = 17.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 38.9 and 21.4.
    \nsubtract the two numbers.
    \n38.9 – 21.4 = 17.5.<\/p>\n

    Question 10.
    \n576 +94.6<\/p>\n

    Answer:
    \n576 + 94.6 = 670.6.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 576 and 94.6.
    \nadd the two numbers.
    \n576 + 94.6 = 670.6.<\/p>\n

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

    In 11-18, estimate each sum or difference.<\/p>\n

    Question 11.
    \n79.1 + 32.4<\/p>\n

    Answer:
    \n79.1 + 32.4 = 111.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 79.1 and 32.4.
    \nadd the two numbers.
    \n79.1 + 32.4 = 111.5.<\/p>\n

    Question 12.
    \n788.9 – 572<\/p>\n

    Answer:
    \n788.9 – 572 = 216.9.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 788.9 and 572.
    \nsubtract the two numbers.
    \n788.9 – 572 = 216.9.<\/p>\n

    Question 13.
    \n837 + 488.12<\/p>\n

    Answer:
    \n837 + 488.12 = 1325.12<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 837 and 488.12.
    \nadd the two numbers.
    \n837 + 488.12 = 1325.12.<\/p>\n

    Question 14.
    \n418.5 \u2013 23.7<\/p>\n

    Answer:
    \n418.5 – 23.7 = 394.8.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 418.5 and 23.7.
    \nsubtract the two numbers.
    \n418.5 – 23.7 = 394.8.<\/p>\n

    Question 15.
    \n2.9 + 3.9<\/p>\n

    Answer:
    \n2.9 + 3.9 = 6.8.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 2.9 and 3.9.
    \nadd the two numbers.
    \n2.9 – 3.9 = 6.8.<\/p>\n

    Question 16.
    \n$12.99 – $3.95<\/p>\n

    Answer:
    \n$12.99 – $3.95 = 9.04.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 12.99 and 3.95.
    \nsubtract the two numbers.
    \n12.99 – 3.95 = 9.04.<\/p>\n

    Question 17.
    \n8.1 + 3.7 + 7.9.<\/p>\n

    Answer:
    \n8.1 + 3.7 + 7.9 = 19.7.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe three numbers are 8.1, 3.7, and 7.9.
    \nadd the three numbers.
    \n8.1 + 3.7 = 11.8.
    \n7.9 + 11.8 = 19.7.<\/p>\n

    Question 18.
    \n3.8 + 4.1 + 3.3<\/p>\n

    Answer:
    \n3.8 + 4.1 + 3.3 = 11.2.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe three numbers are 3.8, 4.1, and 3.3.
    \nadd the three numbers.
    \n3.8 + 4.1 = 7.9.
    \n3.3 + 7.9 = 11.2.<\/p>\n

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

    Question 19.
    \nConstruct Arguments<\/strong> The cost of one DVD is $16.98, and the cost of another DVD is $9.29. Ed estimated the cost of the two DVDs to be about $27. Is his estimate higher or lower than the actual cost? Explain.<\/p>\n

    Answer:
    \nThe estimate is equal.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe cost of one DVD is $16.98, and the cost of another DVD is $9.29.
    \nEd estimated the cost of the two DVDs to be about $27.
    \n16.98 + 9.29 = 26.27.
    \nthe estimate is equal to the actual cost.<\/p>\n

    Question 20.
    \nHigher Order Thinking<\/strong> A teacher is organizing a field trip. Each bus can seat up to 46 people. Is it better to estimate a greater or lesser number than the actual number of people going on the field trip? Why?<\/p>\n

    Answer:
    \nThe estimation is lesser than the actual number of people going on the field trip.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA teacher is organizing a field trip.
    \nEach bus can seat up to 46 people.
    \nthe estimate a lesser number than the actual number of people going on the field trip.<\/p>\n

    Question 21.
    \nThe size and shape of Golden Gate Park are often compared to the size and shape of Central Park. About how many more acres does Golden Gate Park cover than Central Park?
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of acres does Golden Gate Park covers than central park = 174 acres.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe size and shape of Golden Gate Park are often compared to the size and shape of the central park.
    \nthe central park in New York City has an area of 843 acres.
    \nGolden Gate Park in San Francisco, California, has an area of 1,017 acres.
    \n1017 – 843 = 174.
    \nso the number of acres does Golden Gate Park covers than central park = 174.<\/p>\n

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

    Question 22.
    \nThree rock samples have masses of 74.05 grams, 9.72 grams, and 45.49 grams. A scientist estimates the total mass of the samples by rounding each mass to the nearest whole number. Which lists the numbers he will add?
    \nA. 75, 10, and 46
    \nB. 74.1, 9.7, and 45.5
    \nC. 74, 10, and 45
    \nD. 75, 10, and 50<\/p>\n

    Answer:
    \nOption A is the correct answer.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThree rock samples have masses of 74.05 grams, 9.72 grams, and 45.49 grams.
    \nA scientist estimates the total mass of the samples by rounding each mass to the nearest whole number.
    \n74.05 = 75.
    \n9.72 = 10.
    \n45.49 = 46.
    \nso option A is the correct answer.<\/p>\n

    Question 23.
    \nUmberto buys a game for $7.89 and some batteries for $5.49. He pays with a $20 bill. Which is the best estimate of how much change he should get?
    \nA. $5.00
    \nB. $7.00
    \nC. $13.00
    \nD. $17.00<\/p>\n

    Answer:
    \nThe better estimate of change he should get = $7.00.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nUmberto buys a game for $7.89 and some batteries for $5.49.
    \nHe pays with a $20 bill.
    \n7.89 + 5.49 = 13.38.
    \n20 – 13.38 = 6.62.
    \nso option B is correct.<\/p>\n

    Lesson 2.3 Use Models to Add and Subtract Decimals<\/h3>\n

    Solve & Share<\/strong>
    \nGloria rode her bicycle 0.75 mile in the morning and 1.40 miles in the afternoon. How many miles did Gloria ride in all? Solve this problem any way you choose.<\/p>\n

    You can use tools, such as place-value blocks, to help determine how many miles Gloria rode.
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of miles did Gloria ride in all = 2.15.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nGloria rode her bicycle 0.75 miles in the morning and 1.40 miles in the afternoon.
    \n0.75 + 1.40 = 2.15.
    \nso the number of miles did Gloria ride in all = 2.15.<\/p>\n

    Look Back!<\/strong> Make Sense and Persevere<\/strong> How can you check that your answer is reasonable?<\/p>\n

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

    Essential Question<\/strong>
    \nHow Can You Use Models to Add Decimals?<\/p>\n

    A.<\/strong>
    \nUse the table at the right to find the total monthly cost of using the dishwasher and the DVD player.<\/p>\n

    \"Envision
    \nPlace-value blocks can be used to add decimals.
    \n\"Envision<\/p>\n

    Use compatible numbers to estimate. $0.85 + $0.40 is about $0.80 + $0.40, so the sum is about $1.20.<\/p>\n

    B.<\/strong>
    \nUse place-value blocks to model $0.85 + $0.40.
    \n\"Envision<\/p>\n

    C.<\/strong>
    \nCombine the blocks. Regroup when you can.
    \n\"Envision
    \nThe monthly cost of using the dishwasher and DVD player is $1.25.<\/p>\n

    Convince Me!<\/strong> Critique Reasoning For the example above, Jesse said, “The total monthly cost of using the ceiling light and the dishwasher was $0.74.” Is Jesse correct? Explain.<\/p>\n

    Answer:
    \nNo, Jesse was not correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe total monthly cost of using the ceiling light and the dishwasher was $0.74.
    \nthe total monthly cost of using the ceiling light = $0.89.
    \nthe total monthly cost of using the dishwasher = $0.85.
    \n0.89 + 0.85 = 1.74.
    \nso Jesse was not correct.<\/p>\n

    Another Example<\/strong>
    \nYou can subtract decimals with place-value blocks. Find 1.57 – 0.89.<\/p>\n

    Step 1<\/strong>
    \nShow 1.57 with place-value blocks.
    \n\"Envision<\/p>\n

    Step 2<\/strong>
    \nTo subtract 0.89, regroup the blocks and remove 8 tenths and 9 hundredths. The blocks remaining are the difference.
    \n\"Envision<\/p>\n

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

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

    Question 1.
    \nExplain how to use place-value blocks to find the difference between the monthly cost of using the DVD player and the dishwasher. Then find the difference.<\/p>\n

    Answer:
    \nThe difference between the DVD player and the dishwasher = $0.45.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe cost of a DVD player is $0.40.
    \nthe cost of the dishwasher is $0.85.
    \n0.85-0.40 = 0.45.
    \nso the difference between DVD player and the dishwasher = $0.45.<\/p>\n

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

    In 2-7, use place-value blocks to add or subtract.<\/p>\n

    Question 2.
    \n1.22 +0.34<\/p>\n

    Answer:
    \n1.22 + 0.34 = 1.56.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 1.22 and 0.34.
    \nadd the two numbers.
    \n1.22 + 0.34 = 1.56.<\/p>\n

    Question 3.
    \n0.63 +0.41<\/p>\n

    Answer:
    \n0.63 + 0.41 = 1.04.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 0.63 and 0.41.
    \nadd the two numbers.
    \n0.63 + 0.41 = 1.04.<\/p>\n

    Question 4.
    \n2.73 \u2013 0.94<\/p>\n

    Answer:
    \n2.73 – 0.94 = 1.99.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 2.73 and 0.94.
    \nsubtract the two numbers.
    \n2.73 – 0.94 = 1.99.<\/p>\n

    Question 5.
    \n$1.38 \u2013 $0.73<\/p>\n

    Answer:
    \n$1.38 – $0.73 = $0.65.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 1.38 and 0.73.
    \nsubtract the two numbers.
    \n1.38 – 0.73 = $0.65.<\/p>\n

    Question 6.
    \n0.47 \u2013 0.21<\/p>\n

    Answer:
    \n0.47 – 0.21 = 0.26.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 0.47 and 0.21.
    \nsubtract the two numbers.
    \n0.47 – 0.21 = 0.26.<\/p>\n

    Question 7.
    \n2.02 + 0.8<\/p>\n

    Answer:
    \n2.02 + 0.8 = 2.82.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 2.02 and 0.8.
    \nadd the two numbers.
    \n2.02 + 0.8 = 2.82.<\/p>\n

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

    In 8-11, add or subtract. Use place-value blocks to help.<\/p>\n

    Question 8.
    \n0.1 + 0.73<\/p>\n

    Answer:
    \n0.1 + 0.73 = 0.83.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 0.1 and 0.73.
    \nadd the two numbers.
    \n0.1 + 0.73 = 0.83.<\/p>\n

    Question 9.
    \n$1.33 \u2013 $0.35<\/p>\n

    Answer:
    \n$1.33 – $0.35 = 0.98.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 1.33 and 0.35.
    \nsubtract the two numbers.
    \n1.33 – 0.35 = $0.98.<\/p>\n

    Question 10.
    \n$0.37 + $0.47<\/p>\n

    Answer:
    \n$0.37 + $0.47 = $0.84.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are $0.37 and 0.47.
    \nadd the two numbers.
    \n0.37 + 0.47 = 0.84.<\/p>\n

    Question 11.
    \n1.11 +0.89<\/p>\n

    Answer:
    \n1.11 + 0.89 = 2.00.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 1.11 and 0.89.
    \nadd the two numbers.
    \n1.11 + 0.89 = 2.<\/p>\n

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

    Question 12.
    \nConstruct Arguments How is adding 4.56 + 2.31 similar to adding $2.31 + $4.56?<\/p>\n

    Answer:
    \n4.56 + 2.31 is equal to 2.31 + 4.56.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 4.56 and 2.31.
    \nadd the two numbers.
    \n2.31 + 4.56 = 6.87.<\/p>\n

    Question 13.
    \nWrite an expression that is represented by the model below.
    \n\"Envision<\/p>\n

    Answer:
    \nThe number is 1.45.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthere is one hundred blocks.
    \n1.
    \nthere are 4 tens blocks.
    \n0.4.
    \nthere are 5 ones blocks.
    \n1 + 0.4 + 0.05 = 1.45.<\/p>\n

    Question 14.
    \nWithout adding the decimals, tell if the sum of 0.46 + 0.25 is less than or greater than 1? Explain.<\/p>\n

    Answer:
    \nThe sum is greater than 1.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n0.46 + 0.25 = 0.71.
    \n46 + 25 = 71.
    \n71 is greater than 1.
    \nso the sum is greater than 1.<\/p>\n

    Question 15.
    \nNumber Sense<\/strong> Estimate to decide if the sum of 314 + 175 is more or less than 600.<\/p>\n

    Answer:
    \nThe sum is less than 600.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 314 + 175 = 489.
    \n489 is less than 600.
    \nso the sum is less than 600.<\/p>\n

    Question 16.
    \nHigher Order Thinking<\/strong> Do you think the difference of 1.4 – 0.95 is less than or greater than 1? Explain.<\/p>\n

    Answer:
    \nThe difference of 1.4 and 0.95 = 0.45.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 1.4 and 0.95 = 489.
    \n0.45 is less than 1.
    \nso the difference is less than 1.<\/p>\n

    Question 17.
    \nVocabulary<\/strong> Estimate 53.8 – 27.6. Circle the compatible numbers to substitute.
    \n54 \u2013 28 53 \u2013 28 55 \u2013 27 55 \u2013 25<\/p>\n

    Answer:
    \nThe numbers are 54 – 28 = 26.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe numbers are 53.8 and 27.6.
    \nthe numbers are 54-28, 53-28, 55-27, and 55-26.
    \n53.8 is equal to 54.
    \n27.6 is equal to 28.
    \n54 – 28 = 26.<\/p>\n

    Question 18.
    \nAlgebra<\/strong> Write an expression that can be used to find the perimeter of the pool shown to the right. Remember, perimeter is the distance around a figure.
    \n\"Envision<\/p>\n

    Answer:
    \nThe perimeter of the figure = 1250 sq m.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe length and breadth of the rectangle.
    \nl = 50 m.
    \nb = 25 m.
    \narea = l x b.
    \narea of the rectangle = l x b.
    \n50 x 25 = 1250.
    \nso the perimeter of the figure = 1250 sq m.<\/p>\n

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

    Question 19.
    \nEach set of place-value blocks below represents a decimal.
    \n\"Envision<\/p>\n

    Part A<\/strong>
    \nWhat is the sum of the decimals?
    \nPart B<\/strong>
    \nExplain how you found your answer.<\/p>\n

    Answer:
    \n0.3 + 0.01 = 0.31.
    \n0.7 + 0.05 = 0.75.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthere are 3 tens blocks.
    \nthere are 2 one’s blocks.
    \n0.3 + 0.01 = 0.31.
    \nthere are 7 tens blocks.
    \nthere are 5 ones blocks.
    \n0.7 + 0.05 = 0.75.<\/p>\n

    Lesson 2.4 Use Strategies to Add Decimals<\/h2>\n

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

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

    Mr. Davidson has two sacks of potatoes. The first sack weighs 11.39 pounds. The second sack weighs 14.27 pounds. How many pounds of potatoes does Mr. Davidson have in all? Solve this problem any way you choose.<\/p>\n

    You can generalize what you know about whole number addition to decimal addition
    \n\"Envision<\/p>\n

    Look Back!<\/strong> How is adding decimals similar to adding whole numbers?<\/p>\n

    Answer:
    \nThe number of pounds of potatoes does Mr. Davidson has in all = 25.66.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nMr. Davidson has two sacks of potatoes.
    \nThe first sack weighs 11.39 pounds.
    \nThe second sack weighs 14.27 pounds.
    \n11.39 + 14.27 = 25.66.
    \nso the number of pounds of potatoes does Mr. Davidson has in all = 25.66.<\/p>\n

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

    Essential Question<\/strong> How Can You Add Decimals?<\/p>\n

    A.<\/strong>
    \nA swim team participated in a relay race. The swimmers’ times for each leg of the race were recorded in a table. What was the combined time for Caleb and Bradley’s legs of the relay race?<\/p>\n

    You can find 21.39 + 21.59, but estimate first: 21 + 22 = 43.
    \n\"Envision
    \n\"Envision<\/p>\n

    B.<\/strong>
    \nStep 1<\/strong>
    \nJust like with whole numbers, line up the addends by place value. The decimal points will also line up.
    \n\"Envision<\/p>\n

    C.
    \nStep 2<\/strong>
    \nUse what you know about partial sums to add the hundredths, tenths, ones, and tens.
    \n\"Envision
    \nThe combined time for Caleb and Bradley was 42.98 seconds. The sum is close to the estimate.<\/p>\n

    Adding decimals is just like adding whole numbers!
    \n\"Envision<\/p>\n

    Convince Me!<\/strong> Critique Reasoning<\/strong> Andr\u00e9 said the last two legs of the race took 3,938 seconds. What mistake did he make?<\/p>\n

    Another Example<\/strong>
    \nCarson ran 7.81 miles last week. He ran 14 miles this week. How many miles did he run in the two weeks?<\/p>\n

    Use properties and a number line to find the sum.
    \n7.81 + 14 = 14 + 7.81 (Commutative Property)
    \n= 14 + (7 + 0.81)
    \n= (14 + 7) + 0.81 (Associative Property)
    \n= 21 + 0.81
    \n= 21.81
    \n\"Envision
    \nCarson ran 21.81 miles in all.
    \nA number line can help you visualize adding decimals.
    \n\"Envision<\/p>\n

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

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

    Question 1.
    \nHow is adding 21.39 + 21.59 like adding 2,139 + 2,159?<\/p>\n

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

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 21.39 and 21.59.
    \nadd two numbers.
    \n21.39 + 21.59 = 42.98.
    \n2139 + 2159 = 4298.
    \nso both are the same.<\/p>\n

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

    In 2-5, use place value and properties to find each sum.<\/p>\n

    Question 2.
    \n0.82 + 4.21<\/p>\n

    Answer:
    \n0.82 + 4.21 = 5.03.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 0.82 and 4.21.
    \nadd the two numbers.
    \n0.82 + (4 + 0.21).
    \n(0.82 + 0.21) + 4.
    \n1.03 + 4.
    \n5.03.<\/p>\n

    Question 3.
    \n9.1 + 7.21<\/p>\n

    Answer:
    \n9.1 + 7.21 = 16.31.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 9.1 and 7.21.
    \nadd the two numbers.
    \n9.1 + (7 + 0.21).
    \n(9.1 + 0.21) + 7.
    \n9.31 + 7.
    \n16.31.<\/p>\n

    Question 4.
    \n0.26 + 8.3<\/p>\n

    Answer:
    \n0.26 + 8.3 = 8.56.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 0.26 and 8.3.
    \nadd the two numbers.
    \n0.26 + (8 + 0.3).
    \n(0.26 + 0.3) + 8.
    \n0.56 + 8.
    \n8.56.<\/p>\n

    Question 5.
    \n4.98 + 3.02<\/p>\n

    Answer:
    \n4.98 + 3.02 = 8.00.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 4.98 and 3.02.
    \nadd the two numbers.
    \n4.98 + (3 + 0.2).
    \n(4.98 + 0.2) + 3.
    \n5 + 3.
    \n8.<\/p>\n

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

    You can estimate first to be sure your answers are reasonable.
    \n\"Envision<\/p>\n

    Leveled Practice<\/strong> In 6-12, use place value and properties of operations to find each sum.<\/p>\n

    Question 6.
    \n\"Envision<\/p>\n

    Answer:
    \n1.03 + 0.36 = 1.39.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 1.03 and 0.36.
    \nadd the two numbers.
    \n0.36 + (1 + 0.3).
    \n(0.36 + 0.3) + 1.
    \n0.96 + 1.
    \n1.03 + 0.36 = 1.39.
    \n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-2-<\/p>\n

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

    Answer:
    \n6.9 + 2.8 = 9.7.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 6.9 and 2.8.
    \nadd the two numbers.
    \n6.9 + (2 + 0.8).
    \n(6.9 + 0.8) + 2.
    \n7.7 + 2.
    \n6.9 + 2.8 = 9.7<\/p>\n

    \"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-2-<\/p>\n

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

    Answer:
    \n45.08 + 2.01 = 47.09.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 45.08 and 2.01.
    \nadd the two numbers.
    \n45.08 + (2 + 0.1).
    \n(45.08 + 0.1) + 2.
    \n45.09 + 2.
    \n45.08 + 2.01 = 47.09.
    \n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-2-<\/p>\n

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

    Answer:
    \n2.00 + 0.78 = 2.78.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 2.00 and 0.78.
    \nadd the two numbers.
    \n0.78 + (1 + 1.0).
    \n(0.78 + 1.0) + 1.
    \n1.78 + 1.
    \n2.00 + 0.78 = 2.78.
    \n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-2-<\/p>\n

    Question 10.
    \n$271.90 + $34.22<\/p>\n

    Answer:
    \n$271.90 + $34.22 = $316.12.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are $271.90 and $34.22.
    \nadd the two numbers.
    \n271.90 + (34 + 0.22).
    \n(271.90 + 0.22) + 34.
    \n272.12 + 34.
    \n$271.90 + $34.22 = $316.12.<\/p>\n

    Question 11.
    \n7.2 + 3.96 + 8.8<\/p>\n

    Answer:
    \n7.2 + 3.96 + 8.8 = 19.96.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 7.2, 88, and 3.96.
    \nadd the three numbers.
    \n7.2 + (88 + 3.96).
    \n(7.2 + 3.96) + 88.
    \n1.16 + 88.
    \n7.2 + 3.96 + 8.8 = 19.96.<\/p>\n

    Question 12.
    \n16.62 + 4 + 2.38<\/p>\n

    Answer:
    \n16.62 + 4 + 2.38 = 23.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 16.62,4 and 2.38.
    \nadd the two numbers.
    \n16.62 + (4 + 2.38).
    \n(16.62 + 4) + 2.38.
    \n16.66 + 2.38.
    \n16.62 + 4 + 2.38\u00a0 = 23.<\/p>\n

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

    Question 13.
    \nA farmer sold 53.2 pounds of carrots and 29.4 pounds of asparagus to a restaurant. How many pounds of these two vegetables did the restaurant buy?
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of pounds of these two vegetables did the restaurant buy = 82.6.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA farmer sold 53.2 pounds of carrots and 29.4 pounds of asparagus to a restaurant.
    \nthe two numbers are 53.2 and 29.4.
    \n53.2 + 29.4 = 82.6.
    \nso the number of pounds of these two vegetables did the restaurant buy = 82.6.<\/p>\n

    For 14 and 15, use the table.<\/p>\n

    Question 14.
    \nenVision\u00ae STEM<\/strong> Which two cities have the greatest combined rainfall for a typical year?<\/p>\n

    Answer:
    \nThe two cities have the greatest combined rainfall for a typical year =<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe cities that have the rainfall are:
    \nMacon 45 inches.
    \nBoise 12.19 inches.
    \nCaribou 37.44 inches.
    \nSpringfield 44.97 inches.
    \nthe two cities that have the greater rainfall are Caribou and Springfield.<\/p>\n

    Question 15.
    \nNumber Sense<\/strong> Which location had less than 45 inches of rain but more than 40 inches of rain?
    \n\"Envision<\/p>\n

    Answer:
    \nThe location that had less than 45 inches of rain but more than 40 inches of rain = Springfield, MO.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe cities that have the rainfall are:
    \nMacon 45 inches.
    \nBoise 12.19 inches.
    \nCaribou 37.44 inches.
    \nSpringfield 44.97 inches.
    \n44.97 < 45.
    \n44.97 > 40.
    \nso the location that had less than 45 inches of rain but more than 40 inches of rain = Springfield, MO.<\/p>\n

    Question 16.
    \nHigher Order Thinking<\/strong> Tim earned $16 babysitting and $17.50 mowing a lawn. He paid $8.50 for a movie and bought a small popcorn for $1.95. Write an expression to show how much money he has left.<\/p>\n

    Answer:
    \nThe expression to show how much money he has left = $43.95.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nTim earned $16 babysitting and $17.50 mowing a lawn.
    \nHe paid $8.50 for a movie and bought a small popcorn for $1.95.
    \n$16 + $17.50 + $8.50 + $1.95.
    \n$16 + $17.50 = 33.5.
    \n$8.50 + $1.95 = 10.45.
    \n$33.5 + 10.45 = $43.95.<\/p>\n

    Question 17.
    \nCritique Reasoning<\/strong> Juan adds 3.8 + 4.6 and gets a sum of 84. Is his answer correct? Tell how you know.<\/p>\n

    Answer:
    \nNo, he was not correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nJuan adds 3.8 + 4.6 and gets a sum of 84.
    \n3.8 + 4.6 = 8.4.
    \nthe sum is the same but the values are not the same.
    \nso he was not correct.<\/p>\n

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

    Question 18.
    \nChoose all expressions that are equal to 12.9.
    \n\"Envision 0.02 + 12 + 0.88
    \n\"Envision 0.06 + 12.03
    \n\"Envision 11.9 + 1
    \n\"Envision 6.2 + 3.4 + 2.3
    \n\"Envision 3.01 + 2.01 + 7.7<\/p>\n

    Answer:
    \nOptions A and B are correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe expressions are 0.02 + 12 + 0.88.
    \n0.02 + 12 = 12.02.
    \n12.02 + 0.88 = 12.90.
    \n11.9 + 1 = 12.9.
    \nso the options A and B are correct.<\/p>\n

    Question 19.
    \nChoose all expressions that are equal to 16.02.
    \n\"Envision 16 + 0.02
    \n\"Envision 3.42 + 8 + 4.6
    \n\"Envision 16.01 + 1
    \n\"Envision 12.06 + 3.14
    \n\"Envision 7.36 +8.66<\/p>\n

    Answer:
    \nOptions A and B are correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe expressions are 16 + 0.02.
    \n16.02.
    \n3.42 + 8 + 4.6 = 16.02.
    \nso options A and B are correct.<\/p>\n

    Lesson 2.5 Use Strategies to Subtract Decimals<\/h3>\n

    Solve & Share<\/strong>
    \nMs. Garcia is an electrician and has a length of wire that is 32.7 meters long. She has another length of wire that is 15.33 meters long. How much longer is one wire than the other? Solve this problem any way you choose.<\/p>\n

    You can use what you know about whole number subtraction to subtract decimals.
    \n\"Envision<\/p>\n

    Answer:
    \nThe longer is one wire than the other = 17.37 meters.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nMs. Garcia is an electrician and has a length of wire that is 32.7 meters long.
    \nShe has another length of wire that is 15.33 meters long.
    \n15.33 + 32.7 = 48.03.
    \n32.7 – 15.33 = 17.37.
    \nso the longer is one wire than the other = 17.37 meters.<\/p>\n

    Look Back!<\/strong> Use Structure How can you use the relationship between addition and subtraction to check your work above?<\/p>\n

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

    Essential Question<\/strong>
    \nHow Can You Subtract Decimals?<\/p>\n

    A.<\/strong>
    \nWhat is the difference in the wingspans of the two butterflies?
    \n\"Envision
    \nEstimate before you find the exact answer.
    \n6 – 4 = 2
    \n\"Envision<\/p>\n

    B.<\/strong>
    \nYou can use a number line to subtract.
    \n\"Envision<\/p>\n

    C.<\/strong>
    \nHere’s one way to subtract using partial differences.
    \nFind 5.92 \u2013 4.37
    \n\"Envision
    \n5.92 \u2013 4.37 = 1.55<\/p>\n

    Convince Me!<\/strong> Be Precise in the solution above, what strategies can you use to subtract the 7 hundredths?<\/p>\n

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

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

    Question 1.
    \nHow can you use addition to check that 1.55 cm is the difference in the wingspans of the two butterflies?<\/p>\n

    Answer:
    \nThe answers are 3.00 and 1.45.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 3.00 and 1.45.
    \n3.00 – 1.45 = 1.55.
    \nso the difference is 1.55.
    \nthe answers are 3.00 and 1.45.<\/p>\n

    Question 2.
    \nMaria rewrote 45.59 \u2013 7.9 as 45.59 \u2013 7.90. Did she change the value of 7.9 by placing the zero after 7.9? Why or why not?<\/p>\n

    Answer:
    \nYes, she changed the value of 7.9 by placing the zero.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nMaria rewrote 45.59 \u2013 7.9 as 45.59 \u2013 7.90.
    \n45.59 – 7.9 = 37.69.
    \nyes, she changed the value of 7.9 by placing the zer0.<\/p>\n

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

    In 3-10, subtract the decimals.<\/p>\n

    Question 3.
    \n16.82 \u2013 5.21<\/p>\n

    Answer:
    \n16.82 – 5.21 = 11.61.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that
    \nthe two numbers are 16.82 and 5.21.
    \nsubtract the numbers.
    \n16.82 – 5.21 = 11.61.<\/p>\n

    Question 4.
    \n7.21 \u2013 6.1<\/p>\n

    Answer:
    \n7.21 – 6.1 = 1.1.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that
    \nthe two numbers are 7.21 and 6.1.
    \nsubtract the numbers.
    \n7.21 – 6.1 = 1.1.<\/p>\n

    Question 5.
    \n23.06 \u2013 8.24<\/p>\n

    Answer:
    \n23.06 – 8.24 = 14.82<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that
    \nthe two numbers are 23.06 and 8.24.
    \nsubtract the numbers.
    \n23.06 – 8.24 = 14.82.<\/p>\n

    Question 6.
    \n$4.08 \u2013 $2.12<\/p>\n

    Answer:
    \n$4.08 – $2.12 = $1.96.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that
    \nthe two numbers are $4.08 and $2.12.
    \nsubtract the numbers.
    \n$4.08 – $2.12 = $1.96.<\/p>\n

    Question 7.
    \n56.8 – 2.76<\/p>\n

    Answer:
    \n56.8 – 2.76 = 54.04.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that
    \nthe two numbers are 56.8 and 2.76.
    \nsubtract the numbers.
    \n56.8 – 2.76 = 54.04.<\/p>\n

    Question 8.
    \n$43.80 \u2013 $16.00<\/p>\n

    Answer:
    \n$43.80 – $16.00 = $27.8.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that
    \nthe two numbers are $43.80 and $16.00.
    \nsubtract the numbers.
    \n$43.80 – $16.00 = $27.8.<\/p>\n

    Question 9.
    \n22.4 \u2013 10.7<\/p>\n

    Answer:
    \n22.4 – 10.7 = 11.7.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that
    \nthe two numbers are 22.4 and 10.7.
    \nsubtract the numbers.
    \n22.4 – 10.7 = 11.7.<\/p>\n

    Question 10.
    \n$36.40 – $21.16<\/p>\n

    Answer:
    \n$36.40 – $21.16 = $15.24.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that
    \nthe two numbers are $36.40 and $21.16.
    \nsubtract the numbers.
    \n$36.40 – $21.16 = $15.24.<\/p>\n

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

    Leveled Practice<\/strong> In 11-26, find the difference.<\/p>\n

    Question 11.
    \n7.8 \u2013 4.9<\/p>\n

    Answer:
    \n7.8 – 4.9 = 2.9.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that
    \nthe two numbers are 7.8 and 4.9.
    \nsubtract the numbers.
    \n7.8 – 4.9 = 2.9.<\/p>\n

    Question 12.
    \n$20.60 \u2013 $14.35<\/p>\n

    Answer:
    \n$20.60 – $14.35 = $6.25.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that
    \nthe two numbers are $20.60 and $14.35.
    \nsubtract the numbers.
    \n$20.60 – $14.35 = $6.25.<\/p>\n

    Question 13.
    \n43.90 \u2013 7.52<\/p>\n

    Answer:
    \n43.90 – 7.52 = 36.38.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that
    \nthe two numbers are 43.90 and 7.52.
    \nsubtract the numbers.
    \n43.90 – 7.52 = 36.38.<\/p>\n

    Question 14.
    \n65.90 \u2013 28.38<\/p>\n

    Answer:
    \n65.90 – 28.38 = 37.52.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that
    \nthe two numbers are 65.90 and 28.38.
    \nsubtract the numbers.
    \n65.90 – 28.38 = 37.52.<\/p>\n

    Question 15.
    \n15.03 \u2013 4.12<\/p>\n

    Answer:
    \n15.03 – 4.12 = 10.91.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that
    \nthe two numbers are 15.03 and 4.12.
    \nsubtract the numbers.
    \n15.03 – 4.12 = 10.91.<\/p>\n

    Question 16.
    \n13.9 \u2013 3.8<\/p>\n

    Answer:
    \n13.9 – 3.8 = 10.1.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that
    \nthe two numbers are 13.9 and 3.8.
    \nsubtract the numbers.
    \n13.9 – 3.8 = 10.1.<\/p>\n

    Question 17.
    \n65.18 \u2013 12.05<\/p>\n

    Answer:
    \n65.18 – 12.05 = 53.13.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that
    \nthe two numbers are 65.18 and 12.05.
    \nsubtract the numbers.
    \n65.18 – 12.05 = 53.13.<\/p>\n

    Question 18.
    \n$52.02 \u2013 $0.83<\/p>\n

    Answer:
    \n$52.02 – $0.83 = $51.19.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that
    \nthe two numbers are $52.02 and $0.83.
    \nsubtract the numbers.
    \n$52.02 – $0.83 = $51.19.<\/p>\n

    Question 19.
    \n7.09 \u2013 3.65<\/p>\n

    Answer:
    \n7.09 – 3.65 = 3.44.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that
    \nthe two numbers are 7.09 and 3.65.
    \nsubtract the numbers.
    \n7.09 – 3.65 = 3.44.<\/p>\n

    Question 20.
    \n34.49 \u2013 12.61<\/p>\n

    Answer:
    \n34.49 – 12.61 = 21.88<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that
    \nthe two numbers are 34.49 and 12.61.
    \nsubtract the numbers.
    \n34.49 – 12.61 = 21.88.<\/p>\n

    Question 21.
    \n85.22 \u2013 43.5<\/p>\n

    Answer:
    \n85.22 – 43.5 = 41.72.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that
    \nthe two numbers are 85.22 and 43.5.
    \nsubtract the numbers.
    \n85.22 – 43.5 = 41.72.<\/p>\n

    Question 22.
    \n$10.05 \u2013 $4.50<\/p>\n

    Answer:
    \n$10.05 – $4.50 = $5.55.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that
    \nthe two numbers are $10.05 and $4.50.
    \nsubtract the numbers.
    \n$10.05 – $4.50 = $5.55.<\/p>\n

    Question 23.
    \n5.27 \u2013 3.4<\/p>\n

    Answer:
    \n5.27 – 3.4 = 1.87.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that
    \nthe two numbers are 5.27 and 3.4.
    \nsubtract the numbers.
    \n5.27 – 3.4 = 1.87<\/p>\n

    Question 24.
    \n23.6 \u2013 8.27<\/p>\n

    Answer:
    \n23.6 – 8.27 = 15.33.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that
    \nthe two numbers are 23.6 and 8.27.
    \nsubtract the numbers.
    \n23.6 – 8.27 = 15.33.<\/p>\n

    Question 25.
    \n8.04 \u2013 0.3<\/p>\n

    Answer:
    \n8.04 – 0.3 = 7.74.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that
    \nthe two numbers are 8.04 and 0.3.
    \nsubtract the numbers.
    \n8.04 – 0.3 = 7.74.<\/p>\n

    Question 26.
    \n$21.37 \u2013 $10.95<\/p>\n

    Answer:
    \n$21.37 – $10.95 = $10.42.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that
    \nthe two numbers are $21.37 and $10.95.
    \nsubtract the numbers.
    \n$21.37 – $10.95 = $10.42.<\/p>\n

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

    Question 27.
    \nAlgebra<\/strong> The Pyramid of Khafre measured 143.5 meters high. The Pyramid of Menkaure measured 65.5 meters high. Write and solve an equation to find d, the difference in the heights of these two pyramids.
    \n\"Envision<\/p>\n

    Answer:
    \nThe difference in the heights of these two pyramids = 143.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe Pyramid of Khafre measured 143.5 meters high.
    \nThe Pyramid of Menkaure measured 65.5 meters high.
    \n143.5 – 65.5 = 78.
    \n78 + 65.5 = 143.5.
    \nso the difference in the heights of these two pyramids = 143.5.<\/p>\n

    Question 28.
    \nHigher Order Thinking<\/strong> Jonah bought a 1.5-liter bottle of seltzer. He used 0.8 liter of seltzer in some punch. Which is greater, the amount he used or the amount he has left? Explain how you decided<\/p>\n

    Answer:
    \nThe amount he used is greater.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nJohan bought a 1.5-liter bottle of seltzer.
    \nHe used 0.8 liters of seltzer in some punch.
    \n1.5 – 0.8 = 0.7.
    \nthe amount he used is greater.<\/p>\n

    Question 29.
    \nSue subtracted 2.9 from 20.9 and got 1.8. Explain why this is not reasonable.<\/p>\n

    Answer:
    \n2.9 – 20.9 = 18.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nSue subtracted 2.9 from 20.9 and got 1.8.
    \n2.9 and 2.9 is the difference and got 1.8.
    \n2.9 – 20.9 = 18.
    \nso this is not reasonable.<\/p>\n

    Question 30.
    \nMake Sense and Persevere<\/strong> Abe had $156.43 in his bank account at the beginning of the month. He made the two withdrawals shown in his check register. How much money does he have left in his bank account? He must have at least $100 in his account by the end of the month or he will be charged a fee. How much money does he need to deposit to avoid being charged a fee?
    \n\"Envision<\/p>\n

    Answer:
    \nThe money does he need to deposit to avoid being charged a fee = $60.59.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAbe had $156.43 in his bank account at the beginning of the month.
    \nHe made the two withdrawals shown in his check register.
    \n$156.43 + $17.85 = $174.28.
    \n100 – 39.41 = 60.59.
    \nso the money does he need to deposit to avoid being charged a fee = $60.59.<\/p>\n

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

    Question 31.
    \nCircle all of the subtraction problems with a difference of 1.65.
    \n27.30 \u2013 16.65
    \n11.23 \u2013 9.58
    \n40.4 – 23.9
    \n12.68 – 2.03
    \n21.74 \u2013 20.09<\/p>\n

    Answer:
    \nThe subtraction problems with a difference of 1.65 is second and fifth expression.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n27.30 – 16.65 = 10.65.
    \n11.23 – 9.58 = 1.65.
    \n40.4 – 23.9 = 16.5.
    \n12.68 – 2.03 = 10.65.
    \n21.74 – 20.09 = 1.65.<\/p>\n

    Lesson 2.6 Model with Math<\/p>\n

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

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

    Solve & Share<\/strong>
    \nAt a baseball game, Sheena bought a sandwich for $6.95 and two pretzels for $2.75 each. She paid with a $20 bill. How much change did she receive? Solve this problem any way you choose. Use bar diagrams to help.
    \n\"Envision<\/p>\n

    Answer:
    \nThe change did she receive = $10.3.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAt a baseball game, Sheena bought a sandwich for $6.95 and two pretzels for $2.75 each.
    \nShe paid with a $20 bill.
    \n$6.95 + $2.75 = $9.7.
    \n$20 – $9.7 = $10.3.
    \nso the change did she recieve = $10.3.
    \n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-2-<\/p>\n

    Thinking Habits<\/strong><\/p>\n

    Be a good thinker!
    \n\u2022 These questions can help you. How can I use math I know to help solve the 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> Model with Math<\/strong> What other way can you represent this problem situation?<\/p>\n

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

    Essential Question<\/strong> How Can You Represent a Problem with Bar Diagrams?<\/p>\n

    A.<\/strong>
    \nMonica wants to buy all of the art supplies shown on this sign. She has a coupon for $5.50 off the cost of her purchases. What will Monica’s total cost be after the discount?
    \n\"Envision<\/p>\n

    Model with math<\/strong> means you apply math you have learned to solve problems.
    \n\"Envision<\/p>\n

    What do I need to do to solve the problem?
    \nI need to find Monica’s cost for the art supplies.<\/p>\n

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

    B.<\/strong>
    \nHow can I model with math?<\/strong>
    \nI can<\/strong>
    \n\u2022 use the math I know to help solve the problem.
    \n\u2022 find and answer any hidden questions.
    \n\u2022 use bar diagrams and equations to represent and solve this problem.<\/p>\n

    C.<\/strong>
    \nI will use bar diagrams to represent this situation.
    \n\"Envision
    \n$59.95 + $24.95 + $9.75 + $13.50 = $108.15
    \nThe total cost before the discount is $108.15.
    \n\"Envision
    \n$108.15 – $5.50 = $102.65
    \nMonica’s cost after the discount is $102.65.<\/p>\n

    Convince Me! Model with Math<\/strong> How could you decide if your answer makes sense?<\/p>\n

    Guided Practice<\/strong>
    \nModel with Math<\/strong> Nate has $30.50. He wants to buy his dog a sweater that costs $15, a toy that costs $3.79, and a leash that costs $14.79. How much more money does he need?<\/p>\n

    Answer:
    \nThe more money does he need = $3.08.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nNate has $30.50.
    \nHe wants to buy his dog a sweater that costs $15.
    \na toy that costs $3.79, and a leash that costs $14.79.
    \n$15 + $3.79 + $14.79 = 33.58.
    \n33.58 – 30.50 = 3.08.
    \nso the more money does he need = $3.08.<\/p>\n

    When you model with math you use the math you already know to solve new problems!
    \n\"Envision<\/p>\n

    Question 1.
    \nWhat do you need to find before you can solve the problem?<\/p>\n

    Answer:
    \nThe more money does he need = $3.08.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nNate has $30.50.
    \nHe wants to buy his dog a sweater that costs $15.
    \na toy that costs $3.79, and a leash that costs $14.79.
    \n$15 + $3.79 + $14.79 = 33.58.
    \n33.58 – 30.50 = 3.08.
    \nso the more money does he need = $3.08.<\/p>\n

    Question 2.
    \nDraw bar diagrams to represent the problem and then solve the problem. Show the equations you used to solve the problem.<\/p>\n

    Answer:
    \nThe more money does he need = $3.08.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nNate has $30.50.
    \nHe wants to buy his dog a sweater that costs $15.
    \na toy that costs $3.79, and a leash that costs $14.79.
    \n$15 + $3.79 + $14.79 = 33.58.
    \n33.58 – 30.50 = 3.08.
    \nso the more money does he need = $3.08.<\/p>\n

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

    Model with Math<\/strong>
    \nLuz Maria has $15. She buys a ticket to a movie and a smoothie. How much money does she have left?
    \n\"Envision<\/p>\n

    Question 3.
    \nWhat do you need to find before you can solve the problem?<\/p>\n

    Answer:
    \nThe money does she have left = 412.35.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nLuz Maria has $15.
    \nShe buys a ticket to a movie and a smoothie.
    \n$9.50 + $2.85 = $12.35.
    \nso the money does she have left = $12.35.<\/p>\n

    Question 4.
    \nDraw two bar diagrams to represent the problem.<\/p>\n

    Answer:
    \nThe money does she have left = 412.35.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nLuz Maria has $15.
    \nShe buys a ticket to a movie and a smoothie.
    \n$9.50 + $2.85 = $12.35.
    \nso the money does she have left = $12.35.
    \n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-2-<\/p>\n

    Question 5.
    \nWhat is the solution to the problem? Show the equations you used to solve the problem.<\/p>\n

    Answer:
    \nThe money does she have left = 412.35.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nLuz Maria has $15.
    \nShe buys a ticket to a movie and a smoothie.
    \n$9.50 + $2.85 = $12.35.
    \nso the money does she have left = $12.35.<\/p>\n

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

    Performance Task<\/strong><\/p>\n

    School Trip<\/strong>
    \nAudrey is saving for a school trip. She needs $180 for the bus tickets, $215 for the hotel, and $80 for meals. The table shows how much money she and her sister, Kelsey, have saved over a 4-month period. How much more money does Audrey need for the trip?<\/p>\n

    \"Envision<\/p>\n

    Question 6.
    \nMake Sense and Persevere<\/strong> What are you trying to find?<\/p>\n

    Answer:
    \nThe more money does Audrey needs for the trip = $143.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAudrey is saving for a school trip.
    \nShe needs $180 for the bus tickets, $215 for the hotel, and $80 for meals.
    \n$68 + $31.50 + $158 + $74.75 = 332.25.
    \n180 + 215 + 80 = 475.
    \n475 – 332 = 143.
    \nso the more money does Audrey needs for the trip = $143.<\/p>\n

    Question 7.
    \nConstruct Arguments<\/strong> Should you multiply Audrey’s savings for September by 4 since there are 4 months? Explain.<\/p>\n

    Answer:
    \nNo, we cannot multiply by 4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAudrey’s savings for September is $68.
    \n$68 x 4 = $272.
    \nso we cannot multiply by 4.<\/p>\n

    You can model with math by using what you know about adding and subtracting whole numbers to add and
    \nsubtract decimals.
    \n\"Envision<\/p>\n

    Question 8.
    \nModel with Math<\/strong> Draw bar diagrams to represent the total cost of Audrey’s trip and the total she has saved. Then find the total cost and total savings.<\/p>\n

    Answer:
    \nThe total cost of Audrey’s trip is 332.25.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe total she has saved = 332.25.
    \nthe total cost of Audrey’s trip = 332.25.<\/p>\n

    Question 9.
    \nModel with Math<\/strong> Write and solve an equation to determine how much more money Audrey needs for the trip.<\/p>\n

    Answer:
    \nThe more money Audrey needs for the trip = 475.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAudrey is saving for a school trip.
    \nShe needs $180 for the bus tickets, $215 for the hotel, and $80 for meals.
    \n$68 + $31.50 + $158 + $74.75 = 332.25.
    \n180 + 215 + 80 = 475.
    \n475 – 332 = 143.
    \nso the more money does Audrey needs for the trip = $143.<\/p>\n

    Topic 2 Fluency Review Activity<\/h3>\n

    Point & Tally<\/strong><\/p>\n

    Find a partner. Get paper and a pencil. Each partner chooses either light blue or dark blue.
    \nPartner 1 and Partner 2 each point to a black number at the same time. Each partner subtracts the lesser number from the greater number.
    \nIf the answer is on your color, you get a tally mark. Work until one partner has twelve tally marks.
    \n\"Envision<\/p>\n

    \"Envision<\/p>\n

    Topic 2 Vocabulary Review<\/strong><\/p>\n

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

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

    Word List<\/strong>
    \n\u2022 Associative Property of Addition
    \n\u2022 Commutative Property of Addition
    \n\u2022 compatible numbers
    \n\u2022 compensation
    \n\u2022 equivalent decimals
    \n\u2022 inverse operations<\/p>\n

    Choose the best term from the Word List. Write it on the blank.<\/p>\n

    Question 1.
    \nWhen you adjust one number and change another number in the problem to make a computation easier, you use ____.<\/p>\n

    Answer:
    \nWe will use the compensation.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nwhen you adjust one number and change another number in the problem to make computation easier.
    \nfor example:
    \n2 + 3 + 4.
    \n2 + (3 + 4).
    \n(2 + 3) + 4.
    \n5 + 4 = 9.
    \nso we will use the compensation.<\/p>\n

    Question 2.
    \nYou can replace the values in a problem with _____ so that it’s easier to use mental math to complete the computation.<\/p>\n

    Answer:
    \nWe can replace the values in a problem with compatible numbers.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nyou can replace the values in a problem with compatible numbers.
    \nfor example:
    \n3.9 = 4.
    \n4.8 = 5.
    \n4 + 5 = 9.
    \nso we can replace the values in a problem with compatible numbers.<\/p>\n

    Question 3.
    \nTo align decimal points in a decimal addition problem, annex zeros to write ____ so that all addends have the same number of decimal places.<\/p>\n

    Answer:
    \nTo align decimal points in a decimal addition problem, annex zeros to write compensation so that all addends have the same number of decimal places.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nfor example:
    \n2.99 + 3.79.
    \n3 + 4 = 7.<\/p>\n

    Question 4.
    \nBecause of the ____, I know that 477.75 + (76.89 + 196.25) = (76.89 + 196.25) + 477.75 without adding.<\/p>\n

    Answer:
    \nWe can use associative and commutative properties.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n477.75 + (76.89 + 196.25).
    \n(76.89 + 196.25) + 477.75.
    \nso we can use associative and commutative properties.<\/p>\n

    Question 5.
    \nCross out the numbers below that are NOT equivalent to 500.0.
    \n500.00 5 \u00d7 10 5 \u00d7 102<\/sup> 50.05 500.500<\/p>\n

    Answer:
    \n500, 5 x 10 x 10.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe numbers are 500, 5 x 10, 5 x 10 x 10, 50.05.
    \n5 x 10 x 10 = 500.
    \nso the numbers that are not equivalent to 500.<\/p>\n

    Question 6.
    \nCross out the numbers below that are NOT equivalent to 53.2 + 16.8.
    \n7 \u00d7 101<\/sup> 0.070 7.0 7 \u00d7 7 (7 \u00d7 10) + (0 \u00d7 1)<\/p>\n

    Circle the problem that uses compensation.<\/p>\n

    Question 7.
    \n32.7 + 15.6 = 32.6 + 15.7 45.7 + 26.2 = 45.7 + 26.3 \u2013 0.1<\/p>\n

    Answer:
    \nYes, this problem uses the compensation.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe expressions are 32.7 + 15.6 = 32.6 + 15.7.
    \n45.7 + 26.2 = 45.7 + 26.3 – 0.1.
    \nso this uses a compensation.<\/p>\n

    Question 8.
    \n14.24 \u2013 11.8 = 14.24 – 12 + 0.2 168.3 \u2013 53.8 = 168.3 \u2013 53.4 \u2013 0.4<\/p>\n

    Answer:
    \nYes this problem also uses the compensation.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe expressions are 14.24 – 11.8.
    \n14.24 – 12 + 0.2.
    \n168.3 – 53.8 = 168.3 – 53.4 – 0.4.
    \nso this problem also uses the compensation method.<\/p>\n

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

    Question 9.
    \nExplain how the Commutative Property of Addition, the Associative Property of Addition and mental math can help you find 75.2 + (57.376 + 24.8). What is the sum?<\/p>\n

    Answer:
    \nThe sum is 157.376.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nby using the Associative property of addition and Commutative property of addition.
    \n75.2 + (57.376 + 24.8).
    \n(75.2 + 57.376) + 24.8.
    \n132.576 + 24.8 = 157.376.
    \nso the sum is 157.376.<\/p>\n

    Topic 2 Reteaching<\/h3>\n

    Set A<\/strong>
    \npages 45-48
    \nAdd 15.3 + 1.1 + 1.7 using mental math.<\/p>\n

    15.3 and 1.7 are compatible numbers because they are easy to calculate mentally.
    \nThe Commutative Property of Addition enables us to add in any order.
    \n15.3 + 1.1 + 1.7 = 15.3 + 1.7 + 1.1
    \n= 17.0 + 1.1
    \n= 18.1<\/p>\n

    Remember<\/strong> that you can use compatible numbers or compensation to find sums and differences.
    \nUse mental math to add or subtract.<\/p>\n

    Question 1.
    \n8.6 + 23.4 + 1.4<\/p>\n

    Answer:
    \n8.6 + 23.4 + 1.4 = 33.4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nby using the Associative property of addition and Commutative property of addition.
    \n8.6 + (23.4 + 1.4).
    \n(8.6 + 23.4) + 1.4.
    \n32 + 1.4 = 33.4.<\/p>\n

    Question 2.
    \n27 \u2013 9.9<\/p>\n

    Answer:
    \n27 – 9.9 = 17.1.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nby using the Associative property of addition and Commutative property of subtraction.
    \n27 – 9.9 = 17.1.<\/p>\n

    Question 3.
    \n13.5 + 5.7 + 36.5<\/p>\n

    Answer:
    \n13.5 + 5.7 + 36.5 = 55.7.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nby using the Associative property of addition and Commutative property of addition.
    \n13.5 + (5.7 + 36.5).
    \n(13.5 + 5.7) + 36.5.
    \n19.2 + 36.5 = 55.7.<\/p>\n

    Question 4.
    \n205.4 – 99.7<\/p>\n

    Answer:
    \n205.4 – 99.7 = 105.7.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 205.4 and 99.7.
    \nsubtract the numbers.
    \n205.4 – 99.7 = 105.7.<\/p>\n

    Set B<\/strong>
    \npages 49-52<\/p>\n

    Estimate 22.4 \u2013 16.2.
    \n\"Envision
    \n22.4 \u2013 16.2 is about 5.<\/p>\n

    Remember<\/strong> that compatible numbers can give a different estimate than rounding. Estimate each sum or difference.<\/p>\n

    Question 1.
    \n358 + 293<\/p>\n

    Answer:
    \n358 + 293 = 651.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 358 + 293.
    \nadd the two numbers.
    \n358 + 293 = 651.<\/p>\n

    Question 2.
    \n15.01 \u2013 4.4<\/p>\n

    Answer:
    \n15.01 – 4.4 = 10.61.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 15.01 and 4.4.
    \nsubtract the two numbers.
    \n15.01 – 4.4 = 10.61.<\/p>\n

    Question 3.
    \n80.01 + 2.89<\/p>\n

    Answer:
    \n80.01 + 2.89 = 82.9.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 80.01 and 2.89.
    \nadd the two numbers.
    \n80.01 + 2.89 = 82.9.<\/p>\n

    Question 4.
    \n25,003 \u2013 12,900<\/p>\n

    Answer:
    \n25003 – 12900 = 12103.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 25003 and 12900.
    \nsubtract the two numbers.
    \n25003 – 12900 = 12103.<\/p>\n

    Set C<\/strong>
    \npages 53-56<\/p>\n

    Use place-value blocks to subtract 1.86 \u2013 0.95.<\/p>\n

    Show 1 flat, 8 longs, and 6 small squares to represent 1.86.
    \n\"Envision<\/p>\n

    Remove 9 tenths and 5 hundredths, regrouping as needed.
    \n\"Envision<\/p>\n

    Count what is left.
    \n1.86 – 0.95 = 0.91
    \n\"Envision<\/p>\n

    Add or subtract. Use place-value blocks for help.<\/p>\n

    Question 1.
    \n0.02 + 0.89<\/p>\n

    Answer:
    \n0.02 + 0.89 = 0.91.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 0.02 and 0.89.
    \nadd the two numbers.
    \n0.02 + 0.89 = 0.91.<\/p>\n

    Question 2.
    \n0.67 \u2013 0.31<\/p>\n

    Answer:
    \n0.67 – 0.31 = 0.36.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 15.01 and 4.4.
    \nsubtract the two numbers.
    \n0.67 – 0.31 = 0.36.<\/p>\n

    Question 3.
    \n0.34 + 0.34<\/p>\n

    Answer:
    \n0.34 + 0.34 = 0.68.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 0.34 and 0.34.
    \nadd the two numbers.
    \n0.34 + 0.34 = 0.68.<\/p>\n

    Question 4.
    \n0.81 \u2013 0.78<\/p>\n

    Answer:
    \n0.81 – 0.78 = 0.03.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 0.81 and 0.78.
    \nsubtract the two numbers.
    \n0.81 – 0.78 = 0.03.<\/p>\n

    Set D<\/strong>
    \npages 57-60, 61-64<\/p>\n

    Lucy bought 2.12 pounds of pears and 3 pounds of apples. Find how many more pounds of apples than pears Lucy bought.
    \nUse place-value blocks to help.
    \n\"Envision<\/p>\n

    Add or subtract. Use place-value blocks to help.<\/p>\n

    Question 1.
    \n7.06 + 0.85<\/p>\n

    Answer:
    \n7.06 + 0.85 = 7.91.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 7.06 and 0.85.
    \nadd the two numbers.
    \n7.06 + 0.85 = 7.91.<\/p>\n

    Question 2.
    \n24.07 \u2013 5.31<\/p>\n

    Answer:
    \n24.07 – 5.31 = 18.76.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 24.07 and 5.31.
    \nsubtract the two numbers.
    \n24.07 – 5.31 = 18.76.<\/p>\n

    Question 3.
    \n51.92 \u2013 28.03<\/p>\n

    Answer:
    \n51.92 – 28.03 = 23.89.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 51.92 and 28.03.
    \nsubtract the two numbers.
    \n51.92 – 28.03 = 23.89.<\/p>\n

    Question 4.
    \n8.71 – 0.4<\/p>\n

    Answer:
    \n8.71 – 0.4 = 8.31.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 8.71 and 0.4.
    \nsubtract the two numbers.
    \n8.71 – 0.4 = 8.31.<\/p>\n

    Question 5.
    \n98 + 3.79<\/p>\n

    Answer:
    \n98 + 3.79 = 101.79.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 98 and 3.79.
    \nadd the two numbers.
    \n98 + 3.79 = 101.79.<\/p>\n

    Question 6.
    \nTalia measured two strings. The green string was 2.37 cm long. The blue string was 4 cm long. How many centimeters longer was the blue string than the green string?<\/p>\n

    Answer:
    \nThe number of centimeters longer was the blue string than the green string = 1.63 cm long.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nTalia measured two strings.
    \nThe green string was 2.37 cm long.
    \nThe blue string was 4 cm long.
    \n4 – 2.37 = 1.63.
    \nso the number of centimeters longer was the blue string than the green string = 1.63 cm long.<\/p>\n

    Set E<\/strong>
    \npages 65-68
    \nThink about these questions to help you model with math.<\/p>\n

    Thinking Habits<\/strong>
    \n\u2022 How can I use math I know to help solve the 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

    Remember<\/strong> a good model clearly shows how the quantities in the problem are related. Alberto ran 15.6 km on Monday, 12.8 km on Tuesday, and 6.5 km on Wednesday. Dennis ran 11.25 km on Monday, 14.6 km on Tuesday, and 8 km on Wednesday. Who ran farther? How much farther?<\/p>\n

    Question 1.
    \nWhat do you need to find before you can solve the problem?<\/p>\n

    Answer:
    \nAlberto ran farther than Dennis.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAlberto ran 15.6 km on Monday, 12.8 km on Tuesday, and 6.5 km on Wednesday.
    \nDennis ran 11.25 km on Monday, 14.6 km on Tuesday, and 8 km on Wednesday.
    \n15.6 + 12.8 + 6.5 = 34.9.
    \n11.25 + 14.6 + 8 = 33.85.
    \nAlberto ran farther than Dennis.
    \n34.9 – 33.85 = 1.05.<\/p>\n

    Question 2.
    \nWrite equations to model this problem. Then solve the problem.<\/p>\n

    Answer:
    \nAlberto ran farther than Dennis.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAlberto ran 15.6 km on Monday, 12.8 km on Tuesday, and 6.5 km on Wednesday.
    \nDennis ran 11.25 km on Monday, 14.6 km on Tuesday, and 8 km on Wednesday.
    \n15.6 + 12.8 + 6.5 = 34.9.
    \n11.25 + 14.6 + 8 = 33.85.
    \nAlberto ran farther than Dennis.
    \n34.9 – 33.85 = 1.05.<\/p>\n

    Topic 2 Assessment Practice<\/h3>\n

    Question 1.
    \nKayla’s dollhouse has 15.15 square feet downstairs and 6.45 square feet upstairs. What is the estimated total area if you round the decimals to the nearest tenth?
    \nA. 21.0
    \nB. 21.6
    \nC. 21.7
    \nD. 22.0<\/p>\n

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

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nKayla’s dollhouse has 15.15 square feet downstairs and 6.45 square feet upstairs.
    \n15.15 = 15.2.
    \n6.45 = 6.5.
    \n15.2 + 6.5 = 21.7.
    \nso option C is correct.<\/p>\n

    Question 2.
    \nEstimate the sum of $12.15, $16.85, and $1.74 by rounding each number to the nearest tenth.
    \nA. $30.70
    \nB. $30.80
    \nC. $31.00
    \nD. $30.00<\/p>\n

    Answer:
    \nOption B was correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nestimate the sum by rounding each number to the nearest tenth.
    \n$12.15 + $16.85 + $1.74 = $30.80.
    \nso option B was correct.<\/p>\n

    Question 3.
    \nWhat is the sum of 2.65 +3.78?
    \nA. 5.33
    \nB. 5.43
    \nC. 6.33
    \nD. 6.43<\/p>\n

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

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 2.65 and 3.78.
    \nadd the two numbers.
    \n2.65 + 3.78 = 6.43.
    \nso option D is correct.<\/p>\n

    Question 4.
    \nWhich decimal makes this equation true? 4.95 + \"Envision = 12.1
    \nA. 7.15
    \nB. 7.85
    \nC. 8.15
    \nD. 8.85<\/p>\n

    Answer:
    \nOption\u00a0 A is correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 4.95 and 12.1.
    \n4.95 – 12.1 = 7.15.
    \nso option A is correct.<\/p>\n

    Question 5.
    \nLawrence spent $1.89 on a bottle of paint and $0.45 on a brush.
    \nA. What was the total amount he spent? Use the model to help you.
    \n\"Envision
    \nB. Explain how the model helps you find the sum.<\/p>\n

    Answer:
    \nThe total amount he spent = $2.34.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nLawrence spent $1.89 on a bottle of paint and $0.45 on a brush.
    \n$1.89 + $0.45 =
    \nso the total amount he spent = $2.34.<\/p>\n

    Question 6.
    \nMatch each expression on the left with the equivalent decimal.
    \n\"Envision<\/p>\n

    Answer:
    \n3.05 + 1.65 = 4.7.
    \n8.5 – 4.8 = 3.7.
    \n4.25 + 1.55 = 5.8.
    \n11.4 – 6.6 = 4.8.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nmatch the expressions on the left with an equivalent symbol.
    \n3.05 + 1.65 = 4.7.
    \n8.5 – 4.8 = 3.7.
    \n4.25 + 1.55 = 5.8.
    \n11.4 – 6.6 = 4.8.<\/p>\n

    Question 7.
    \nEd is training for a race. He ran 12.56 miles on one day, 12.98 miles the second, and 13.04 miles the third day.
    \nA. What is his combined distance for the first three days?
    \nB. How much farther did he run the second day than the first day?<\/p>\n

    Answer:
    \nA. The combined distance for the first three days = 38.58 miles.
    \nB. The farther he runs the second day than the first day = 0.42 miles.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nEd is training for a race.
    \nHe ran 12.56 miles on one day, 12.98 miles on the second, and 13.04 miles on the third day.
    \n12.56 + 12.98 + 13.04 = 38.58.
    \n12.98 – 12.56 = 0.42.
    \nthe combined distance for the first three days = 38.58 miles.
    \nthe farther he runs the second day than the first day = 0.42 miles.<\/p>\n

    Question 8.
    \nThe Thomas Jefferson Memorial is on 18.36 acres of land, the Franklin Delano Roosevelt Memorial is on 7.5 acres of land, the Vietnam Veterans Memorial is on 8.9 acres of land, and the World War I Memorial is on 9.6 acres of land. Which two memorials have the greatest difference in area?
    \nWhat is the difference between the areas of these two memorials? Explain.<\/p>\n

    Answer:
    \nThe difference between the areas of these two memorials = 10.86.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe Thomas Jefferson Memorial is on 18.36 acres of land,
    \nthe Franklin Delano Roosevelt Memorial is on 7.5 acres of land,
    \nthe Vietnam Veterans Memorial is on 8.9 acres of land,
    \nand the World War I Memorial is on 9.6 acres of land.
    \n18.36 – 7.5 = 10.86.
    \n8.9 – 9.6 = 0.7.
    \nso the difference between the areas of these two memorials = 10.86.<\/p>\n

    Question 9.
    \nAmber bought a hardcover book for $23.70 and a paperback for $6.91. How much did she spend in all? If she paid with 2 twenty-dollar bills, how much change did she get?<\/p>\n

    Answer:
    \nThe much change did she get = $10.61.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAmber bought a hardcover book for $23.70 and a paperback for $6.91.
    \n23.70 + 6.91 = 30.61.
    \nIf she paid with 2 twenty-dollar bills.
    \n2 x 20 = 40.
    \n$40 – $30.61 = $10.61.<\/p>\n

    Question 10.
    \nKassandra has a rectangular patio in her backyard. The patio is 12.74 meters long and 5.45 meters wide.
    \n\"Envision
    \nA. Round the length and width to the nearest whole number. Then estimate the perimeter of Kassandra’s patio. Write an equation to model your work.
    \nB. Round the length and width to the nearest tenth. Then estimate the perimeter of Kassandra’s patio. Write an equation to model your work.
    \nC. Find the exact perimeter. Which estimate is closer? Explain why you think that estimate is closer.<\/p>\n

    Answer:
    \nThe length and width to the nearest whole number = 5.5 and 13.
    \nthe length and width to the nearest tenth = 5.5 and 12.7.
    \nthe perimeter is 69.433.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nKassandra has a rectangular patio in her backyard.
    \nThe patio is 12.74 meters long and 5.45 meters wide.
    \nthe nearest whole number is 5.5 and 13.
    \nthe nearest tenth is 5.5 and 12.7.
    \nthe perimeter is 69.433.<\/p>\n

    Topic 2 Performance Task<\/h3>\n

    Video Games<\/strong>
    \nFour students are playing the same video game. Their scores for the first three levels are added together to see if the student has enough points to move on to Round 2.<\/p>\n

    Question 1.
    \nThe students’ scores are shown in the table below.
    \n\"Envision
    \nPart A<\/strong>
    \nA student must have at least 18 points to advance to Round 2. Use estimation to decide if any of the students did not get 18 points.
    \nPart B<\/strong>
    \nUse estimation to decide which student had the greatest number of points. Explain your reasoning.<\/p>\n

    Answer:
    \nThe student has the greater number of points = Zoey.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nkim had 7.18 + 6.55 + 6.45 = 20.18.
    \nSally had 5.49 + 6.18 + 5.72 = 17.39.
    \nTina had 8.02 + 7.94 + 8.38 = 24.34.
    \nzoey had 8.64 + 8.32 + 8.13 = 25.09.<\/p>\n

    Question 2.
    \nComplete the table to find the total number of points for each student.<\/p>\n

    Answer:
    \nThe total number of points of Kim = 20.18.
    \nthe total number of points of Sally = 17.39.
    \nthe total number of points Tina = 24.34.
    \nthe total number of points Zoey = 25.09.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nkim had 7.18 + 6.55 + 6.45 = 20.18.
    \nSally had 5.49 + 6.18 + 5.72 = 17.39.
    \nTina had 8.02 + 7.94 + 8.38 = 24.34.
    \nzoey had 8.64 + 8.32 + 8.13 = 25.09.<\/p>\n

    Question 3.
    \nHow many more points did Zoey score than Sally? Write an equation to model your work.<\/p>\n

    Answer:
    \nThe more points did Zoey score than Sally = 7.7.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nkim had 7.18 + 6.55 + 6.45 = 20.18.
    \nSally had 5.49 + 6.18 + 5.72 = 17.39.
    \nTina had 8.02 + 7.94 + 8.38 = 24.34.
    \nzoey had 8.64 + 8.32 + 8.13 = 25.09.
    \n25.09 – 17.39 = 7.7.<\/p>\n

    Question 4.
    \nUse the total points scored for each student.
    \nPart A<\/strong>
    \nAbout how many points did the four students score in Round 1? Estimate by rounding each point total to the nearest whole number.
    \nPart B<\/strong>
    \nComplete the bar diagram to show the exact total number of points the students scored.
    \n\"Envision<\/p>\n

    Answer:
    \nThe total number of points the students scored = 87.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nkim had 7.18 + 6.55 + 6.45 = 20.18.
    \nSally had 5.49 + 6.18 + 5.72 = 17.39.
    \nTina had 8.02 + 7.94 + 8.38 = 24.34.
    \nzoey had 8.64 + 8.32 + 8.13 = 25.09
    \n20.18 + 17.39 + 24.34 + 25.09 = 87.
    \n\"Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-2-<\/p>\n

    Question 5.
    \nIn Round 2, Zoey had a total of 23.43 points. She got a score of 7.96 in Level 2 and a score of 8.03 in Level 3.
    \nPart A<\/strong>
    \nWhat score did she receive in Level 1?
    \nPart B<\/strong>
    \nExplain how you found your answer.<\/p>\n

    Answer:
    \nIn level 1 Zoey scored 20.18 points.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nZoey had a total of 23.43 points.
    \nShe got a score of 7.96 in Level 2.
    \nthe score of 8.03 in Level 3.
    \n23.43 + 7.96 + 8.03 = 20.18.
    \nso the total score is 20.18 points.<\/p>\n

    Question 6.
    \nKim recorded her scores for Round 2. To estimate her total, she rounds to the nearest whole number and says, “7 + 9 + 7 = 23, so my total is at least 23 points.” Do you agree? Explain your reasoning.
    \n\"Envision<\/p>\n

    Answer:
    \nNo, it was not correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nKim recorded her scores for Round 2.
    \n7 + 9 + 7 = 23.
    \nbut the scores are 6.77, 8.48, and 7.13.
    \n6.77 + 8.48 + 7.13 = 22.38.
    \nso it was not correct.<\/p>\n","protected":false},"excerpt":{"rendered":"

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