Grade 6 Fractions: Complex Fractions

Worked examples

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

1. Example 1

   Simplify the complex fraction (1/3) / (2/5)

   1. A complex fraction has a fraction in its numerator or denominator. Its main fraction bar means divide: (1/3) / (2/5) = 1/3 ÷ 2/5.
   2. Keep the first fraction, change ÷ to ×, and flip the second: 2/5 becomes 5/2.
   3. 1/3 ÷ 2/5 = 1/3 × 5/2.
   4. Multiply the numerators: 1 × 5 = 5. Multiply the denominators: 3 × 2 = 6.
   5. That gives 5/6.
   6. So (1/3) / (2/5) = 5/6.

   Answer: 5/6

2. Example 2

   Simplify the complex fraction (7/8) / (5/12)

   1. A complex fraction has a fraction in its numerator or denominator. Its main fraction bar means divide: (7/8) / (5/12) = 7/8 ÷ 5/12.
   2. Keep the first fraction, change ÷ to ×, and flip the second: 5/12 becomes 12/5.
   3. 7/8 ÷ 5/12 = 7/8 × 12/5.
   4. Multiply the numerators: 7 × 12 = 84. Multiply the denominators: 8 × 5 = 40.
   5. That gives 84/40.
   6. The greatest number that divides both 84 and 40 is 4.
   7. Divide the top and bottom by 4: 84 ÷ 4 = 21 and 40 ÷ 4 = 10, so 84/40 = 21/10.
   8. So (7/8) / (5/12) = 21/10.

   Answer: 21/10

3. Example 3

   Simplify the complex fraction (3/4) / (7/10)

   1. A complex fraction has a fraction in its numerator or denominator. Its main fraction bar means divide: (3/4) / (7/10) = 3/4 ÷ 7/10.
   2. Keep the first fraction, change ÷ to ×, and flip the second: 7/10 becomes 10/7.
   3. 3/4 ÷ 7/10 = 3/4 × 10/7.
   4. Multiply the numerators: 3 × 10 = 30. Multiply the denominators: 4 × 7 = 28.
   5. That gives 30/28.
   6. The greatest number that divides both 30 and 28 is 2.
   7. Divide the top and bottom by 2: 30 ÷ 2 = 15 and 28 ÷ 2 = 14, so 30/28 = 15/14.
   8. So (3/4) / (7/10) = 15/14.

   Answer: 15/14