Grade 5 Fractions: Subtracting Unlike Denominators

Worked examples

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

1. Example 1

   7/8 − 2/3 = ?

   1. The denominators are different, so rename both fractions with a common denominator, 24.
   2. Multiply the top and bottom by 3: 7 × 3 = 21 and 8 × 3 = 24, so 7/8 = 21/24.
   3. Multiply the top and bottom by 8: 2 × 8 = 16 and 3 × 8 = 24, so 2/3 = 16/24.
   4. Subtract the numerators and keep the denominator: 21 − 16 = 5, so the difference is 5/24.
   5. So 7/8 − 2/3 = 5/24.

   Answer: 5/24

2. Example 2

   4/4 − 1/8 = ?

   1. The denominators are different, so rename both fractions with a common denominator, 8.
   2. Multiply the top and bottom by 2: 4 × 2 = 8 and 4 × 2 = 8, so 4/4 = 8/8.
   3. Subtract the numerators and keep the denominator: 8 − 1 = 7, so the difference is 7/8.
   4. So 4/4 − 1/8 = 7/8.

   Answer: 7/8

3. Example 3

   2/2 − 4/6 = ?

   1. The denominators are different, so rename both fractions with a common denominator, 6.
   2. Multiply the top and bottom by 3: 2 × 3 = 6 and 2 × 3 = 6, so 2/2 = 6/6.
   3. Subtract the numerators and keep the denominator: 6 − 4 = 2, so the difference is 2/6.
   4. The greatest number that divides both 2 and 6 is 2.
   5. Divide the top and bottom by 2: 2 ÷ 2 = 1 and 6 ÷ 2 = 3, so 2/6 = 1/3.
   6. So 2/2 − 4/6 = 1/3.

   Answer: 1/3