Lesson 9€¦ · 92 Lesson 9 Add and Subtract Decimals ©Curriculum Associates, LLC Copying is not permitted. Solve. 4 Xavier has three objects in his bag One object weighs 4 05 ounces,

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©Curriculum Associates, LLC Copying is not permitted. 89Lesson 9 Add and Subtract Decimals

Name: Add and Subtract Decimals

Lesson 9

Prerequisite: Adding and Subtracting Decimals

Study the example problem showing how to subtract decimals. Then solve problems 1–5.

1 Explain why you have to use regrouping in the example problem?

2 You can also subtract decimals by writing the problem vertically, lining up the decimal points to keep track of the place values

The problem to the right is partially completed

How does the regrouping shown relate to the place-value method used in the example?

Example

Charlie collected 3 8 pounds of shells at the beach Sebal collected 1 55 pounds of shells How many more pounds did Charlie collect than Sebal?

To solve, subtract 1 55 from 3 8 Use a place-value chart to help Regroup as needed to subtract

ones ? tenths hundredths

Charlie’s shellsregroup as

33

??

87

010

Sebal’s shells 1 ? 5 5

3 ones 2 1 one 5 2 ones7 tenths 2 5 tenths 5 2 tenths10 hundredths 2 5 hundredths 5 5 hundredths

Difference 5 2 ones 1 2 tenths 1 5 hundredths

Charlie collected 2 25 pounds more than Sebal

3 802 1 55

7 10

8989

B

B

Possible answer: 5 hundredths is more than 0 hundredths, so you need more

hundredths in order to take 5 away. You must regroup 1 tenth as 10 hundredths.

Possible answer: The regrouping is the same in each method. The vertical problem

shows that 1 of the tenths was regrouped as 10 hundredths.

©Curriculum Associates, LLC Copying is not permitted.90 Lesson 9 Add and Subtract Decimals

Solve.

3 At a diving competition, Allison scored 78 5 on her fi rst dive Hannah’s score on her fi rst dive was 74 65 How many more points did Allison score on her fi rst dive than Hannah?

Show your work.

Solution:

4 Franklin hiked 1 38 kilometers from the nature center to the waterfall Then he hiked 2 6 kilometers to the bridge Finally, he hiked 3 45 kilometers to return to the nature center How many kilometers did Franklin hike in all?

Show your work.

Solution:

5 Dharma and Jorge are looking at cell phone plans A group plan will cost an average of $135 95 per month An individual plan will cost an average of $72 75 per month Should Dharma and Jorge purchase a group plan or two individual plans? How much money could they save?

Show your work.

Solution:

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Allison scored 3.85 more points than Hannah.

The cost of two individual plans: $72.75 1 $72.75 5 $145.50

Cost of two individual plans 2 cost of group plan: $145.50 2 $135.95 5 $9.55

They could save $9.55 each month with the group plan.

Franklin hiked a total of 7.43 kilometers.

78.502 74.65

3.85

7 14 10

1.382.60

1 3.45

7.43

1 1

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Name: Lesson 9

Adding Decimals to Thousandths

Study the example problem showing how to add decimals to thousandths. Then solve problems 1–6.

1 Estimate the sum in the example problem

2 How does estimating the answer help you to know that you placed the decimal point in the sum correctly?

3 How does adding with decimals compare to adding whole numbers?

Example

Colin found three small rocks He measured the mass of each One rock was 3 56 grams, another was 1 742 grams, and the third rock was 2 4 grams What was the total mass of the three rocks?

Line up the decimal points and write 0s as needed to help you keep the place values aligned Then add

3 5601 742

1 2 400

7 702

1 1

The total mass of the rocks is 7 702 grams

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Possible answer: 4 1 2 1 2 5 8

Possible answer: If the decimal sum is close to my estimate, then I know that I placed

the decimal point in my sum correctly.

Possible answer: The process is the same. The only difference is writing the

decimal point in the sum.

B

B

B


Solve.

4 Xavier has three objects in his bag One object weighs 4 05 ounces, another weighs 2 7 ounces, and the third object weighs 1 985 ounces What is the total weight of the objects in Xavier’s bag?

Show your work.

Solution:

5 To qualify for the long jump competition, an athlete must jump a combined distance of more than 16 meters in 3 jumps Jackie jumped 4 86 meters, 5 428 meters, and 5 9 meters Did Jackie qualify for the competition?

Show your work.

Solution:

6 The lengths of the sides of a triangle are shown What is the perimeter of the triangle?

Show your work.

Solution:

12.4 cm8.73 cm

10.075 cm

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4.0502.700

1 1.985

8.735

1 1

The total weight of the objects is 8.735 ounces.

Yes, Jackie qualified for the competition.

The perimeter is 31.205 centimeters.

4.8605.428

1 5.900

16.188

2

16.188 16

8.73012.400

1 10.075

31.205

1 1 1

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5 Alphonso’s notecard is 7 4 inches wide Oscar’s notecard is 5 872 inches wide Which notecard is wider, and by how much?

6 Ichiro’s batting average in baseball is 0 342 This is 0 08 higher than Giancarlo’s batting average What is Giancarlo’s batting average?

Show your work.

Solution:

7 Sheila is running in a race that is 5 kilometers long After 10 minutes, she has run 1 875 kilometers How much farther does Sheila have to run to fi nish the race?

Show your work.

Solution:

8 In a library, bookcases A, B, C, and D are lined up in order Bookcase A is 1 38 meters from bookcase B and 6 8 meters from bookcase C Bookcase D is 0 925 meters farther from bookcase C than the distance between bookcases B and C How far apart are bookcases C and D?

Show your work.

Solution:

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Alphonso’s notecard is 1.528 inches wider.

Giancarlo’s batting average is 0.262.

Bookcase D is 6.345 meters from bookcase C.

Sheila still has to run 3.125 kilometers.

Distance from bookcase B to C: 6.8 2 1.38 5 5.42

Distance from bookcase C to D: 5.42 1 0.925 5 6.345

0.3422 0.080

0.262

2 14

5.0002 1.875

3.125

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Name: Lesson 9

Subtracting Decimals to Thousandths

Study the example problem showing how to subtract decimals to thousandths. Then solve problems 1–8.

1 Why is it useful to write 6 52 as 6 520?

2 How could you estimate the diff erence?

3 How do you know that the answer to a decimal subtraction problem is reasonable? How can you check that the answer is correct? Explain

4 A gymnast earned a score of 9 438 on the uneven bars and a score of 8 75 on the balance beam How much greater was her score on the uneven bars?

Example

A carpenter has a board that is 6 52 feet long and 1 748 feet wide How much longer is the length than the width?

To solve, find 6 52 2 1 748 Align the decimal points and subtract

The board is 4 772 inches longer than it is wide

6.5 2 02 1.7 4 8

4.7 7 2

5 141110

93

Possible answer: 7 2 2 5 5

Possible answer: Writing the 0 helps with subtracting in the

thousandths place.

The score on the uneven bars was 0.688 greater.

Possible explanation: Estimation can show that my answer is reasonable. Addition is

the opposite of subtraction, so I can add to check the answer.

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Name: Lesson 9

Add and Subtract Decimals

Solve the problems.

3 Terri walked 3 825 miles yesterday Today she walked 5 5 miles How many more miles did Terri walk today than yesterday?

A 1 675 miles C 1 785 miles

B 1 725 miles D 2 325 miles

Brenda chose B as the correct answer How did she get that answer?

2 Jeremy has three pencils One pencil is 9 36 inches long The second pencil is 6 7 inches long The third pencil is 8 025 inches long Will placing the pencils end to end make a total length greater than 2 feet?

Show your work.

Solution:

1 On the fl oor exercise, Nadia scored 9 85 Mary Lou scored 8 975 How much higher was Nadia’s score on the fl oor exercise?

Show your work.

Solution:

You can write 0s to help you keep the place values aligned.

How many inches are there in 2 feet?

Which number is the greater number?

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Nadia’s score was 0.875 higher.

Yes; the length of all three pencils is 0.085 inch more than 2 feet.

Possible answer: Brenda wrote the values in the hundredths and tenths

place from 3.825 in the difference, then subtracted 3.8 from 5.5.

24.085 inches is equal to 2 feet and 0.085 inch.

9.8502 8.975

0.875

8 171410

9.3606.700

1 8.025

24.085

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6 Kristin weighs three kittens at a vet’s clinic The heaviest one weighs 3 28 pounds The heaviest kitten is 1 056 pounds heavier than the medium-weight one The lightest kitten is 1 2 pounds lighter than the medium-weight kitten What is the total weight of the kittens?

Show your work.

Solution:

Solve.

4 Hal’s backpack weighs 3 54 pounds Sarah’s pack weighs 2 129 pounds Frank’s pack weighs 2 8 pounds Select True or False for each statement

a. Hal’s backpack weighs 1 429 pounds more than Sarah’s u True u False

b. The combined weight of the backpacks is more than 8 5 pounds u True u False

c. Frank’s backpack is 0 671 pound heavier than Sarah’s u True u False

d. Hal’s backpack is less than 1 pound heavier than Frank’s u True u False

5 Which of these equals 2 427? Select all that apply

A 1 34 1 1 087

B 1 4 1 1 027

C 8 35 2 5 923

D 6 2 3 573

Be sure that you add or subtract digits with the same place value.

How can you find the weights of the medium-weight and lightest kittens?

Be sure that you choose the correct operation to evaluate each statement.

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Weight of medium-weight kitten: 3.28 2 1.056 5 2.224Weight of lightest kitten: 2.224 2 1.2 5 1.024Total weight 5 1.024 1 2.224 1 3.28 5 6.528

The total weight of the kittens is 6.528 pounds.

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Documents

Lesson 9€¦ · 92 Lesson 9 Add and Subtract Decimals ©Curriculum Associates, LLC Copying is not permitted. Solve. 4 Xavier has three objects in his bag One object weighs 4 05 ounces,