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

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

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

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

Additional Example 1A: Regrouping Mixed Numbers Subtract. Write each answer in simplest form. 1 6 __ 5 6 __ 7 – 2 1 6 __ 7 6 __ 1 6 __ 1 6 __ 6 __ 1 6 __ 7 6 Rename 7 as 6 + 1 = 6 + + . 5 6 __ 5 6 __ Subtract the fractions and then the whole numbers. –2 –2 ______ ______ 2 6 __ 1 3 __ 4 Write the answer in simplest form. = 4

Additional Example 1B: Regrouping Mixed Numbers Subtract. Write each answer in simplest form. 2 5 __ 7 10 __ 8 – 6 4 10 __ 14 10 __ 10 is a multiple of 5, so 10 is a common denominator. 8 7 4 10 __ 7 10 __ 4 10 __ 10 __ 4 10 __ 7 10 __ Rename 8 as 7 + 1 = 7 + + . –6 –6 ______ ______ 7 10 __ Subtract the fractions and then the whole numbers. 1

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

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

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

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

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

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

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

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

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

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

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? 7 10 __ 4 5 __ 4 9 10 __ 4 7 __ 6 7 __ 3 5 7 __ 2 9 __ 1 7 9 __ 3 8 __ 9 16 __ 5 13 16 __ 3 8 __ 5 8 __ 6 cups