5-3 Regrouping to Subtract Mixed Numbers

Learn to regroup mixed numbers to subtract.

5-3 Regrouping to Subtract Mixed Numbers

Jimmy and his mother planted a tree when it was 1 ft tall. Now the tree is 2 ft tall. How much has the tree grown since it was planted?

34__

14__

14__ 3

4__

The difference in the heights can be represented by 2 – 1 .

14__

14__3

4__

You will need to regroup 2 because the fraction in 1 is greater than .

14__Divide one whole of 2 into fourths.

5-3 Regrouping to Subtract Mixed Numbers

2 14__ 1 5

4__

–1

14__

– 1______ ______

= 24__ 1

2__

34__

Regroup 2 as 1 .34__

54__

The tree has grown ft since it was planted.12__

141 1

414

14

14

114

14

14

14

1

1

1414

5-3 Regrouping to Subtract Mixed Numbers

23__

6 5 33__

–3 23__ –3 2

3__

______ ______

2

Subtract the fractions and then the whole numbers.

Write 6 as a mixed number with a denominator of 3. Rename 6 as 5 + .3

3__

13__

6 – 3

6 – 4 = 2 Estimate the difference.

2 is close to the estimate of 2. The answer is reasonable. 13__

Additional Example 1A: Regrouping Mixed Numbers Subtract. Write each answer in simplest form.

5-3 Regrouping to Subtract Mixed NumbersAdditional Example 1B: Regrouping Mixed Numbers

Subtract. Write each answer in simplest form.

13__ 3

4__

5 412__ 4 16

12__

–2 912__ –2 9

12__

______ ______

2 712__ Subtract the fractions and then the

whole numbers.

Rename 5 as 4 + 1 = 4 + + . 412 __ 4

12__ 12

12__ 4

12__

The LCM of 4 and 3 is 12.

5 – 2

5 – 3 = 2 Estimate the difference.

2 is close to the estimate of 2. The answer is reasonable. 712__

5-3 Regrouping to Subtract Mixed NumbersCheck It Out: Example 1A

Subtract. Write each answer in simplest form.

16__ 5

6__

7 16__ 6 7

6__ Rename 7 as 6 + 1 = 6 + + .

–2 5

6__ –2 5

6__

______ ______

4 26__

Subtract the fractions and then the whole numbers.

16__ 1

6__ 6

6__ 1

6__

Write the answer in simplest form.

= 4 13__

7 – 2

7 – 3 = 4 Estimate the difference.

4 is close to the estimate of 4. The answer is reasonable. 13__

5-3 Regrouping to Subtract Mixed Numbers

25__ 7

10__

8 410__ 7 14

10__

Rename 8 as 7 + 1 = 7 + + . –6 710__ –6 7

10__

______ ______

1 710__ Subtract the fractions and then the

whole numbers.

410__ 4

10__ 10

10__ 4

10__

10 is a multiple of 5, so 10 is a common denominator.

8 – 6

8 – 7 = 1 Estimate the difference.

1 is close to the estimate of 1. The answer is reasonable. 710__

Check It Out: Example 1BSubtract. Write each answer in simplest form.

5-3 Regrouping to Subtract Mixed Numbers

Additional Example 2A: Measurement Application

Li is making a quilt. She needs 15 yards of fabric.

Li has 2 yards of fabric. How many more yards does she need?

34__

15 14 44__ Write 15 as a mixed number with a

denominator of 4. Rename 15 as 14 + .

–2 34__ –2 3

4__

______ ______

12

Subtract the fractions and then the whole numbers.

44__

14__

Li needs another 12 yards of fabric.14__

5-3 Regrouping to Subtract Mixed Numbers

Additional Example 2B: Measurement Application

If Li uses 11 yards of fabric, how much of the 15 yards will she have left?

16__

15 14 66__ Write 15 as a mixed number with a

denominator of 6. Rename 15 as 14 + .

–11 16__ –11 1

6__

______ ______

3

Subtract the fractions and then the whole numbers.

66__

56__

Li will have 3 yards of fabric.56__

5-3 Regrouping to Subtract Mixed Numbers

Check It Out: Example 2A

Peggy is making curtains. She needs 13 yards of fabric.

Peggy has 4 yards of fabric. How many more yards does she need?

56__

13 12 66__ Write 13 as a mixed number with a

denominator of 6. Rename 13 as 12 + .

–4 56__ –4 5

6__

______ ______

8

Subtract the fractions and then the whole numbers.

66__

16__

Peggy needs another 8 yards of fabric.16__

5-3 Regrouping to Subtract Mixed Numbers

Check It Out: Example 2B

If Peggy uses 9 yards of fabric, how much of the 13 yards will she have left?

14__

13 12 44__ Write 13 as a mixed number with a

denominator of 4. Rename 13 as 12 + .

–9 14__ –9 1

4__

______ ______

3

Subtract the fractions and then the whole numbers.

44__

34__

Peggy will have 3 yards of fabric left.34__