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5-4

Regrouping to Subtract Mixed Numbers. 5-4. Course 1. Warm Up. Problem of the Day. Lesson Presentation. 2. 2. 3. 11. 9. 9. 11. 1. 4. 1. 1. __. __. __. __. __. __. __. __. __. __. __. 5. 11. 11. 20. 5. 9. 3. 5. 9. 4. 11. Warm Up Add or Subtract.

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5-4

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  1. Regrouping to Subtract Mixed Numbers 5-4 Course 1 Warm Up Problem of the Day Lesson Presentation

  2. 2 2 3 11 9 9 11 1 4 1 1 __ __ __ __ __ __ __ __ __ __ __ 5 11 11 20 5 9 3 5 9 4 11 Warm Up Add or Subtract. 1. 3 + 1 2. 7 + 3. 8 – 2 4. 6 – 1 5 8 5 6

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

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

  5. 5 6 1 1 1 1 5 2 1 7 5 1 __ __ __ __ __ __ __ __ __ __ __ __ 6 6 6 6 6 6 6 3 6 6 6 6 Additional Example 1A: Regrouping Mixed Numbers Subtract. Write each answer in simplest form. 7 – 2 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

  6. 7 2 4 4 7 7 4 10 14 7 4 __ __ __ __ __ __ __ __ __ __ __ 10 10 10 10 10 5 10 10 10 10 10 Additional Example 1B: Regrouping Mixed Numbers Subtract. Write each answer in simplest form. 8 – 6 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

  7. 2 2 1 3 2 3 __ __ __ __ __ __ 3 3 3 3 3 3 Write 6 as a mixed number with a denominator of 3. Rename 6 as 5 + . Additional Example 1C: Regrouping Mixed Numbers Subtract. Write each answer in simplest form. 6 – 3 6 5 Subtract the fractions and then the whole numbers. –3 –3 ______ ______ 2

  8. 9 7 12 9 4 16 4 4 1 3 __ __ __ __ __ __ __ __ __ __ 12 12 12 12 12 12 3 4 12 12 4 __ Rename 5 as 4 + 1 = 4 + + . 12 Additional Example 1D: Regrouping Mixed Numbers Subtract. Write each answer in simplest form. 5 – 2 The LCM of 4 and 3 is 12. 5 4 –2 –2 ______ ______ Subtract the fractions and then the whole numbers. 2

  9. 5 4 1 1 1 1 5 4 1 9 5 1 __ __ __ __ __ __ __ __ __ __ __ __ 8 8 8 8 4 8 8 2 8 8 8 8 Check It Out: Example 1A Subtract. Write each answer in simplest form. 5 – 2 5 4 Rename 5 as 4 + 1 = 4 + + . Subtract the fractions and then the whole numbers. –2 –2 ______ ______ Write the answer in simplest form. 2 = 2

  10. 7 1 2 2 7 7 2 12 14 7 2 __ __ __ __ __ __ __ __ __ __ __ 12 12 12 12 12 6 12 12 12 12 12 Check It Out: Example 1B Subtract. Write each answer in simplest form. 7 – 3 12 is a multiple of 6, so 12 is a common denominator. 7 6 Rename 7 as 6 + 1 = 6 + + . –3 –3 ______ ______ Subtract the fractions and then the whole numbers. 3

  11. 3 3 4 1 4 3 __ __ __ __ __ __ 4 4 4 4 4 4 Check It Out: Example 1C Subtract. Write each answer in simplest form. 5 – 2 Write 5 as a mixed number with a denominator of 4. Rename 5 as 4 + . 5 4 Subtract the fractions and then the whole numbers. –2 –2 ______ ______ 2

  12. 4 1 3 3 2 5 3 6 9 4 3 __ __ __ __ __ __ __ __ __ __ __ 6 6 6 3 6 2 6 6 6 6 6 Check It Out: Example 1D Subtract. Write each answer in simplest form. 8 – 4 The LCM of 2 and 3 is 6. 8 7 Rename 8 as 7 + 1 = 7 + + . –4 –4 ______ ______ Subtract the fractions and then the whole numbers. 3

  13. 3 3 1 1 4 4 3 __ __ __ __ __ __ __ 4 4 4 4 4 4 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.

  14. 1 1 5 5 6 6 1 __ __ __ __ __ __ __ 6 6 6 6 6 6 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.

  15. 5 5 1 1 6 6 5 __ __ __ __ __ __ __ 6 6 6 6 6 6 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.

  16. 1 1 3 3 4 4 1 __ __ __ __ __ __ __ 4 4 4 4 4 4 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.

  17. 9 5 4 6 9 7 7 4 5 2 3 3 1 3 4 __ __ __ __ __ __ __ __ __ __ __ __ 10 8 8 8 9 7 16 10 7 9 7 5 13 __ 5 16 Lesson Quiz Subtract. Write each answer in simplest form. 1. 7 – 3 2. 8 – 3 3. 7 – 5 4. 10 – 4 5. Irena put 10 cups of food in the bird feeder. The birds ate 3 cups. How many cups are left? 6 cups

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