Grade 5 Fractions: Adding Unlike Denominators

Worked examples

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

1. Example 1

   4/8 + 2/3 = ?

   1. The denominators are different, so rename both fractions with a common denominator, 24.
   2. Multiply the top and bottom by 3: 4 × 3 = 12 and 8 × 3 = 24, so 4/8 = 12/24.
   3. Multiply the top and bottom by 8: 2 × 8 = 16 and 3 × 8 = 24, so 2/3 = 16/24.
   4. Add the numerators and keep the denominator: 12 + 16 = 28, so the sum is 28/24.
   5. The greatest number that divides both 28 and 24 is 4.
   6. Divide the top and bottom by 4: 28 ÷ 4 = 7 and 24 ÷ 4 = 6, so 28/24 = 7/6.
   7. So 4/8 + 2/3 = 7/6.

   Answer: 7/6

2. Example 2

   3/6 + 3/4 = ?

   1. The denominators are different, so rename both fractions with a common denominator, 12.
   2. Multiply the top and bottom by 2: 3 × 2 = 6 and 6 × 2 = 12, so 3/6 = 6/12.
   3. Multiply the top and bottom by 3: 3 × 3 = 9 and 4 × 3 = 12, so 3/4 = 9/12.
   4. Add the numerators and keep the denominator: 6 + 9 = 15, so the sum is 15/12.
   5. The greatest number that divides both 15 and 12 is 3.
   6. Divide the top and bottom by 3: 15 ÷ 3 = 5 and 12 ÷ 3 = 4, so 15/12 = 5/4.
   7. So 3/6 + 3/4 = 5/4.

   Answer: 5/4

3. Example 3

   5/8 + 1/4 = ?

   1. The denominators are different, so rename both fractions with a common denominator, 8.
   2. Multiply the top and bottom by 2: 1 × 2 = 2 and 4 × 2 = 8, so 1/4 = 2/8.
   3. Add the numerators and keep the denominator: 5 + 2 = 7, so the sum is 7/8.
   4. So 5/8 + 1/4 = 7/8.

   Answer: 7/8