1. 5-3 Regrouping to Subtract Mixed Numbers Learn to regroup mixed numbers to subtract.

2. 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? 3 4 __ 1 4 1 4 3 4 The difference in the heights can be represented by 2 – 1. 1 4 __ 1 4 3 4 You will need to regroup 2 because the fraction in 1 is greater than. 1 4 __ Divide one whole of 2 into fourths.

3. 5-3 Regrouping to Subtract Mixed Numbers 2 1 4 __ 1 5 4 –1 1 4 __ – 1 ______ = 2 4 __ 1 2 3 4 Regroup 2 as 1. 3 4 __ 5 4 The tree has grown ft since it was planted. 1 2 __ 1414 1 1414 1414 1414 1414 1 1414 1414 1414 1414 1 1 1414 1414

4. 5-3 Regrouping to Subtract Mixed Numbers 2 3 __ 65 3 3 –3 2 3 __ –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 __ 1 3 6 – 3 6 – 4 = 2 Estimate the difference. 2 is close to the estimate of 2. The answer is reasonable. 1 3 __ Additional Example 1A: Regrouping Mixed Numbers Subtract. Write each answer in simplest form.

5. 5-3 Regrouping to Subtract Mixed Numbers Additional Example 1B: Regrouping Mixed Numbers Subtract. Write each answer in simplest form. 1 3 __ 3 4 5 4 12 __ 4 16 12 __ –2 9 12 __ –2 9 12 __ ______ ______ 2 7 12 __ Subtract the fractions and then the whole numbers. Rename 5 as 4 + 1 = 4 + +. 4 12 __ 4 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. 7 12 __

6. 5-3 Regrouping to Subtract Mixed Numbers Check It Out: Example 1A Subtract. Write each answer in simplest form. 1 6 __ 5 6 7 1 6 6 7 6 Rename 7 as 6 + 1 = 6 + +. –2 5 6 __ –2 5 6 __ ______ 4 2 6 __ Subtract the fractions and then the whole numbers. 1 6 __ 1 6 6 6 1 6 Write the answer in simplest form. = 4 1 3 __ 7 – 2 7 – 3 = 4 Estimate the difference. 4 is close to the estimate of 4. The answer is reasonable. 1 3 __

7. 5-3 Regrouping to Subtract Mixed Numbers 2 5 __ 7 10 __ 8 4 10 __ 7 14 10 __ Rename 8 as 7 + 1 = 7 + +. –6 7 10 __ –6 7 10 __ ______ ______ 1 7 10 __ Subtract the fractions and then the whole numbers. 4 10 __ 4 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. 7 10 __ Check It Out: Example 1B Subtract. Write each answer in simplest form.

8. 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? 3 4 __ 1514 4 4 __ Write 15 as a mixed number with a denominator of 4. Rename 15 as 14 +. –2 3 4 __ –2 3 4 __ ______ ______ 12 Subtract the fractions and then the whole numbers. 4 4 __ 1 4 Li needs another 12 yards of fabric. 1 4 __

9. 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? 1 6 __ 1514 6 6 __ Write 15 as a mixed number with a denominator of 6. Rename 15 as 14 +. –11 1 6 __ –11 1 6 __ ______ ______ 3 Subtract the fractions and then the whole numbers. 6 6 __ 5 6 Li will have 3 yards of fabric. 5 6 __

10. 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? 5 6 __ 1312 6 6 __ Write 13 as a mixed number with a denominator of 6. Rename 13 as 12 +. –4 5 6 __ –4 5 6 __ ______ ______ 8 Subtract the fractions and then the whole numbers. 6 6 __ 1 6 Peggy needs another 8 yards of fabric. 1 6 __

11. 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? 1 4 __ 1312 4 4 __ Write 13 as a mixed number with a denominator of 4. Rename 13 as 12 +. –9 1 4 __ –9 1 4 __ ______ ______ 3 Subtract the fractions and then the whole numbers. 4 4 __ 3 4 Peggy will have 3 yards of fabric left. 3 4 __