Grade 6 Fractions: Multiply & Divide Mixed

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   1 1/3 ÷ 3 1/4 = ?

   1. Write 1 1/3 as an improper fraction: 1 × 3 + 1 = 4, so 1 1/3 = 4/3.
   2. Write 3 1/4 as an improper fraction: 3 × 4 + 1 = 13, so 3 1/4 = 13/4.
   3. Keep the first fraction, change ÷ to ×, and flip the second: 13/4 becomes 4/13.
   4. 4/3 ÷ 13/4 = 4/3 × 4/13.
   5. Multiply the numerators: 4 × 4 = 16. Multiply the denominators: 3 × 13 = 39.
   6. That gives 16/39.
   7. So 1 1/3 ÷ 3 1/4 = 16/39.

   Answer: 16/39

2. Example 2

   1 1/6 ÷ 4/5 = ?

   1. Write 1 1/6 as an improper fraction: 1 × 6 + 1 = 7, so 1 1/6 = 7/6.
   2. Keep the first fraction, change ÷ to ×, and flip the second: 4/5 becomes 5/4.
   3. 7/6 ÷ 4/5 = 7/6 × 5/4.
   4. Multiply the numerators: 7 × 5 = 35. Multiply the denominators: 6 × 4 = 24.
   5. That gives 35/24.
   6. 35/24 is more than 1 whole: 35 ÷ 24 = 1 with 11 left over, so 35/24 = 1 11/24.
   7. So 1 1/6 ÷ 4/5 = 1 11/24.

   Answer: 1 11/24

3. Example 3

   1 5/8 × 2/3 = ?

   1. Write 1 5/8 as an improper fraction: 1 × 8 + 5 = 13, so 1 5/8 = 13/8.
   2. Multiply the numerators: 13 × 2 = 26.
   3. Multiply the denominators: 8 × 3 = 24.
   4. 13/8 × 2/3 = 26/24.
   5. The greatest number that divides both 26 and 24 is 2.
   6. Divide the top and bottom by 2: 26 ÷ 2 = 13 and 24 ÷ 2 = 12, so 26/24 = 13/12.
   7. 13/12 is more than 1 whole: 13 ÷ 12 = 1 with 1 left over, so 13/12 = 1 1/12.
   8. So 1 5/8 × 2/3 = 1 1/12.

   Answer: 1 1/12