Hands On: Add and Subtract DecimalsIn this lesson you will use models to add and subtract decimals.

Example 1:

Example 2:

3.80______+ 0.95

7.11______! 6.93

Group 10 dimes to make 1 dollar. Count the money. Solution: $4.75

Change 1 dime into 10 pennies. Change 1 dollar into 10 dimes. Cross out to subtract. Count what’s left. Solution: $0.18

Use models to fi nd the sum or difference. 1. 21.51

________ + 4.50 2. 2.58

_______ + 3.936 3. 5.73

______ ! 0.92 4. 36.86

_______ ! 21.77

Writing Math How is adding decimals similar to adding whole numbers?

12–18 Use with text pages 254–255.ReteachCopyright © Houghton Mifflin Company. All rights reserved.

Name Date

CA StandardsNS 2.1, MR 2.3

Chapter 12, Lesson 1Reteach

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Estimate Sums and DifferencesYou can use rounding to estimate sums or differences. For decimals less than 1, round to the nearest tenth. For decimals greater than 1, round to the nearest whole number.

Estimate 0.576 ! 0.129.

Writing Math If you estimate to the nearest tenth, or to the nearest whole number which method gives you a more exact answer? Explain.

Step 1 Round each number to the nearest tenth.

0.576 " 0.6#

7 > 5, so round up

0.129 " 0.1#

2 < 5, so round down

Step 2 Subtract the rounded numbers.

0.6 _____ ! 0.1 0.5

So, 0.576 ! 0.129 is about 0.5.

Estimate the sum or difference by rounding each number to the nearest tenth. Check that your answer is reasonable.

1. 0.376 ! 0.38 " 2. 44.329 + 12.394 " 3. 28.293 + 32.561 " 4. 14.511 $ 8.633

Estimate the sum or difference by rounding each number to the nearest whole number. Check that your answer is reasonable.

5. 4.935 + 6.83 " 6. 7.873 ! 6.351 " 7. 6.350 + 8.957 " 8. 87.902 $ 52.874

"

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12–24 Use with text pages 256–257.ReteachCopyright © Houghton Mifflin Company. All rights reserved.

Name Date

CA StandardsNS 2.1, MR 2.5

Chapter 12, Lesson 2Reteach

73745_C12L2_RET.indd 12–2473745_C12L2_RET.indd 12–24 12/13/07 4:17:23 AM12/13/07 4:17:23 AM

Add and Subtract DecimalsIn this lesson you will add and subtract decimals and check that your calculations are reasonable.

Add or subtract. Estimate to check your answer.

1. .289

_______ + 3.603 2. 46.581 ________ + 53.959 3. 7.940 _______ ! 4.365 4. 57.032 ________ ! 33.792

Ben’s mom bought 1.4 lb of green grapes and 1.19 lb of red grapes. How manypounds of grapes did she purchase in all?

Step 1 Align the digits in the addends. Use the decimal points as guides. Then add the hundredths.

1.40 ______ +1.19

9

Step 2 Add the tenths.

1.40 ______ +1.19

59

Step 3 Add the ones. Align the decimal point in the sum with the decimal points in the addends.

1.40 ______ +1.19

2.59

Solution:Ben’s mompurchased2.59 lb of grapes.

Check by estimating. 1.4 rounds to 1.1.19 rounds to 1.1 + 1 = 22.59 is close to 2, so my answer is reasonable.

Darnell jogged 1.75 miles on Saturday and 3.56 miles on Sunday. How much farther did Darnell jog on Sunday than Saturday?

Step 1 Align the decimal points. Subtract the hundredths.

3.56 ______ !1.75 1

Step 2Subtract the tenths.

3.56 ______ !1.75 81

Step 3Subtract the ones. Write the decimal point in the answer.

3.56 ______ !1.75

1.81

Solution:Darnell jogged1.81 more miles on Sunday thanSaturday.

Check by estimating. 3.56 rounds to 4.1.75 rounds to 2.4 ! 2 = 21.81 is close to 2, so my answer is reasonable.

2 152 15

Add zeros asnecessary.

5 < 7, so regroup 1 one as 10 tenths.

Writing Math Explain why it is important to line up the decimal points when adding or subtracting decimals.

12–30 Use with text pages 258–261.ReteachCopyright © Houghton Mifflin Company. All rights reserved.

Name Date

CA StandardsNS 2.1, MR 2.1

Chapter 12, Lesson 3Reteach

73745_C12L3_RET.indd 12–3073745_C12L3_RET.indd 12–30 12/4/07 1:37:38 AM12/4/07 1:37:38 AM