Grade 5 Fractions: Mixed Operations

Worked examples

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

1. Example 1

   3/8 − 1/3 = ?

   1. The denominators are different, so rename both fractions with a common denominator, 24.
   2. Multiply the top and bottom by 3: 3 × 3 = 9 and 8 × 3 = 24, so 3/8 = 9/24.
   3. Multiply the top and bottom by 8: 1 × 8 = 8 and 3 × 8 = 24, so 1/3 = 8/24.
   4. Subtract the numerators and keep the denominator: 9 − 8 = 1, so the difference is 1/24.
   5. So 3/8 − 1/3 = 1/24.

   Answer: 1/24

2. Example 2

   1/3 + 2/4 = ?

   1. The denominators are different, so rename both fractions with a common denominator, 12.
   2. Multiply the top and bottom by 4: 1 × 4 = 4 and 3 × 4 = 12, so 1/3 = 4/12.
   3. Multiply the top and bottom by 3: 2 × 3 = 6 and 4 × 3 = 12, so 2/4 = 6/12.
   4. Add the numerators and keep the denominator: 4 + 6 = 10, so the sum is 10/12.
   5. The greatest number that divides both 10 and 12 is 2.
   6. Divide the top and bottom by 2: 10 ÷ 2 = 5 and 12 ÷ 2 = 6, so 10/12 = 5/6.
   7. So 1/3 + 2/4 = 5/6.

   Answer: 5/6

3. Example 3

   2/3 × 1/6 = ?

   1. Multiply the numerators: 2 × 1 = 2.
   2. Multiply the denominators: 3 × 6 = 18.
   3. 2/3 × 1/6 = 2/18.
   4. The greatest number that divides both 2 and 18 is 2.
   5. Divide the top and bottom by 2: 2 ÷ 2 = 1 and 18 ÷ 2 = 9, so 2/18 = 1/9.
   6. So 2/3 × 1/6 = 1/9.

   Answer: 1/9