Year 5 · Mathematics
Fractions for Year 5: equivalent fractions, simplifying and adding
A fraction describes part of a whole that has been split into equal parts. In Year 5, students typically work with equivalent fractions, compare and order fractions, and start adding fractions that share a denominator.
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Try asking: “Explain equivalent fractions”
What the numbers in a fraction mean
In the fraction 3/8, the denominator (bottom number) tells us the whole has been split into 8 equal parts. The numerator (top number) tells us we are talking about 3 of those parts.
The parts must be equal. A pizza cut into 8 uneven slices doesn't show eighths!
Equivalent fractions
Equivalent fractions show the same amount using different numbers. 1/2, 2/4, 3/6 and 4/8 are all equivalent — they each cover exactly half.
To make an equivalent fraction, multiply or divide the numerator and the denominator by the same number. This works because you are really multiplying by a fraction equal to 1, such as 3/3.
Simplifying fractions
Simplifying means finding the equivalent fraction with the smallest possible numbers. Divide the numerator and denominator by a common factor until the only common factor left is 1.
Adding fractions with the same denominator
When the denominators are the same, the parts are the same size, so you just add the numerators and keep the denominator: 2/7 + 3/7 = 5/7.
Students sometimes add the denominators too (2/7 + 3/7 = 5/14). That can't be right — the answer would be smaller than 3/7 on its own!
Finding a fraction of an amount
To find 3/4 of 20, first find 1/4 by dividing by the denominator (20 ÷ 4 = 5), then multiply by the numerator (5 × 3 = 15).
Worked examples
Fill in the missing number: 2/3 = ?/12
- The denominator changed from 3 to 12. 3 × 4 = 12, so it was multiplied by 4.
- Multiply the numerator by 4 as well: 2 × 4 = 8.
Answer: 2/3 = 8/12
Simplify 15/20
- 15 and 20 are both in the 5 times table.
- 15 ÷ 5 = 3 and 20 ÷ 5 = 4.
- 3 and 4 have no common factor other than 1, so we're done.
Answer: 15/20 = 3/4
What is 2/5 of 35?
- Find 1/5 of 35: 35 ÷ 5 = 7.
- Multiply by 2: 7 × 2 = 14.
Answer: 14
Common mistakes to watch for
- Adding the denominators when adding fractions.
- Multiplying only the numerator (or only the denominator) when making equivalent fractions.
- Thinking a bigger denominator means a bigger fraction — 1/8 is smaller than 1/4.
Practice questions
Try these, then reveal the answers. For more questions with hints, use the tutor.
1. Fill in the gap: 1/4 = ?/12
Show answer
3
2. Simplify 6/9
Show answer
2/3
3. What is 3/10 + 4/10?
Show answer
7/10
4. What is 3/4 of 24?
Show answer
18
5. Which is bigger: 2/3 or 5/8?
Show answer
2/3 (2/3 = 16/24 and 5/8 = 15/24)
For parents
How can I help my child understand fractions at home?
Use real objects: fold paper, cut fruit, or share a block of chocolate into equal pieces. Ask questions like 'What fraction is left?' and 'Is 2/4 the same as 1/2?'