Adding fractions · Grade 5
In Grade 5 you learn: adding fractions with related denominators, adding fractions with different denominators, and adding mixed numbers.
You can only add fractions when the pieces are the same size, so the denominators must match. If they don’t, change the fractions to equivalent fractions with a common denominator first, then add the numerators.
Key facts
- Same denominator: add or subtract the tops. The bottom stays the same.
- Different denominators: first change both to a common denominator (the least common multiple is easiest). Then add or subtract.
- Never add the bottoms: 1/2 + 1/3 is not 2/5.
- Mixed numbers: add the wholes and the fractions separately, or turn both into improper fractions.
- If the answer is an improper fraction, you can write it as a mixed number: 19/12 = 1 7/12.
- Simplify the answer at the end.
Worked examples
Example 1
Work out 2/7 + 3/7.
Answer: 5/7
Example 2
Work out 1/5 + 2/5.
Answer: 3/5
Example 3
Work out 3/8 + 1/8.
Answer: 1/2
Example 4
Leo eats 2/8 of a pizza and Amy eats 3/8 of the same pizza. How much of the pizza do they eat altogether?
Answer: 5/8 of the pizza
Example 5
Work out 1/2 + 3/8.
Answer: 7/8
Example 6
Work out 2/3 + 1/4.
Answer: 11/12
Example 7
Work out 3/4 + 5/6.
Answer: 1 7/12
Example 8
Work out 1 3/5 + 2 2/3.
Answer: 4 4/15
Example 9
Work out 1 5/6 + 2 3/4.
Answer: 4 7/12