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Learn to regroup mixed numbers to subtract .

Learn to regroup mixed numbers to subtract. 3. __. 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?. 4. 1. __. 4. The difference in the heights can be represented by 2 – 1. 1. 3. __.

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Learn to regroup mixed numbers to subtract .

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  1. Learn to regroup mixed numbers to subtract.

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

  3. 1 5 __ __ 1 1 1 4 1 5 __ __ 4 4 4 4 3 1 1 4 1 4 1 4 1 4 1 4 3 __ __ 4 4 1 1 4 1 4 1 4 1 4 1 4 1 2 __ __ 2 4 1 __ 2 2 1 Regroup 2 as 1 . –1 – 1 ______ ______ = The tree has grown ft since it was planted.

  4. 2 __ 3 Write 6 as a mixed number with a denominator of 3. Rename 6 as 5 + . 3 __ 3 __ 3 3 2 2 __ __ 3 3 1 __ 3 1 __ 3 Additional Example 1A: Regrouping Mixed Numbers Subtract. Write each answer in simplest form. 6 – 3 Estimate the difference. 6 – 4 = 2 6 5 Subtract the fractions and then the whole numbers. –3 –3 ______ ______ 2 2 is close to the estimate of 2. The answer is reasonable.

  5. 3 1 __ __ 4 3 4 16 __ __ 12 12 4 4 12 4 __ __ __ __ 9 9 __ __ Rename 5 as 4 + 1 = 4 + + . 12 12 12 12 12 12 7 __ 12 7 __ 12 Additional Example 1B: Regrouping Mixed Numbers Subtract. Write each answer in simplest form. 5 – 2 Estimate the difference. 5 – 3 = 2 The LCM of 4 and 3 is 12. 5 4 –2 –2 ______ ______ Subtract the fractions and then the whole numbers. 2 2 is close to the estimate of 2. The answer is reasonable.

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

  7. 2 7 __ __ 5 10 4 14 __ __ 10 10 4 4 4 10 __ __ 7 __ __ 7 __ __ 10 10 10 10 10 10 7 __ 10 7 __ 10 Check It Out: Example 1B Subtract. Write each answer in simplest form. 8 – 6 Estimate the difference. 8 – 7 = 1 10 is a multiple of 5, so 10 is a common denominator. 8 7 Rename 8 as 7 + 1 = 7 + + . –6 –6 ______ ______ Subtract the fractions and then the whole numbers. 1 1 is close to the estimate of 1. The answer is reasonable.

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

  9. 1 __ 6 6 __ 6 __ 6 6 1 1 __ __ 6 6 5 __ 6 5 __ 6 Additional Example 2B: Measurement Application If Li uses 11 yards of fabric, how much of the 15 yards will she have left? Write 15 as a mixed number with a denominator of 6. Rename 15 as 14 + . 15 14 Subtract the fractions and then the whole numbers. –11 –11 ______ ______ 3 Li will have 3 yards of fabric.

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

  11. 1 __ 4 4 __ 4 __ 4 4 1 1 __ __ 4 4 3 __ 4 3 __ 4 Check It Out: Example 2B If Peggy uses 9 yards of fabric, how much of the 13 yards will she have left? Write 13 as a mixed number with a denominator of 4. Rename 13 as 12 + . 13 12 Subtract the fractions and then the whole numbers. –9 –9 ______ ______ 3 Peggy will have 3 yards of fabric left.

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