Year 5 · Mathematics · Number
Fractions
Understand that different fractions can name the same amount, and find and simplify equivalent fractions by multiplying or dividing the numerator and denominator by the same number.
Awaiting educator review. This material was drafted by our content team with AI assistance and is waiting for review by a qualified educator. Please check it suits your child before using it. Created 10 October 2026.
Learning goals
Learners will
- Understand that equivalent fractions name the same amount.
- Create equivalent fractions by multiplying the numerator and denominator by the same number.
- Simplify fractions by dividing the numerator and denominator by a common factor.
Success looks like
- I can explain why 12 and 24 are the same amount.
- I can find a missing number in a pair of equivalent fractions.
- I can write a fraction in its simplest form.
The big idea
A fraction describes equal parts of a whole. In 34, the denominator (4) tells us the whole is split into 4 equal parts, and the numerator (3) tells us we have 3 of those parts.
Try this: fold a strip of paper in half and shade one half. Fold it in half again and open it out. The shaded part is now 24. Fold it once more and you will see 48. The shaded amount never changed, so 12 = 24 = 48. These are equivalent fractions.
Each fold cut every part into smaller equal pieces. The number of parts doubled and the number of shaded parts doubled too. That is why we can make an equivalent fraction by multiplying the numerator and the denominator by the same number. For example, multiply both parts of 23 by 4: 2 × 4 = 8 and 3 × 4 = 12, so 23 = 812.
We can also go the other way. If the numerator and denominator share a common factor, divide both by it. In 69, both 6 and 9 can be divided by 3, giving 23. This is called simplifying. A fraction is in simplest form when the only number that divides into both the numerator and denominator is 1.
- Multiply or divide the numerator and denominator by the same number.
- Never add or subtract the same number from both. Adding 1 to the top and bottom of 12 gives 23, which is a bigger amount, so it is not equivalent.
Equivalent fractions sit at exactly the same point on a number line. If you draw a number line from 0 to 1 marked in halves, another marked in quarters and another in eighths, 12, 24 and 48 all line up.
Worked examples
Making equivalent fractions
Write two fractions that are equivalent to 23.
- Multiply the numerator and denominator by 2: 2 × 2 = 4 and 3 × 2 = 6, giving 46.
- Multiply the numerator and denominator by 4: 2 × 4 = 8 and 3 × 4 = 12, giving 812.
- Both new fractions name the same amount as 23.
Answer: 46 and 812 (other answers such as 69 are also correct).
Finding a missing numerator
Find the missing number: 34 = ?20.
- Look at the denominators. What do we multiply 4 by to get 20? 4 × 5 = 20.
- Do the same to the numerator: 3 × 5 = 15.
- Check: 1520 simplifies back to 34 by dividing both numbers by 5.
Answer: 34 = 1520, so the missing number is 15.
Simplifying a fraction
Write 1216 in simplest form.
- List factors that 12 and 16 share: 1, 2 and 4. The largest is 4.
- Divide both numbers by 4: 12 ÷ 4 = 3 and 16 ÷ 4 = 4.
- 3 and 4 have no common factor other than 1, so we are finished.
Answer: 1216 = 34
Practice check
Have a go, then check your answers. Each answer comes with an explanation.
Answer guide for parents
Which fraction is equivalent to 12?
3/6 — Multiply the numerator and denominator of 12 by 3: 1 × 3 = 3 and 2 × 3 = 6, giving 36.
Which fraction is NOT equivalent to 25?
4/15 — 410, 615 and 820 all come from multiplying 2 and 5 by the same number. 415 does not: the numerator was multiplied by 2 but the denominator by 3.
What is 68 in simplest form?
3/4 — 6 and 8 share a common factor of 2. 6 ÷ 2 = 3 and 8 ÷ 2 = 4, giving 34.
A pizza is cut into 12 equal slices and Ruby eats 3 slices. Which fraction in simplest form shows how much of the pizza Ruby ate?
1/4 — Ruby ate 312 of the pizza. Dividing 3 and 12 by 3 gives 14.
Find the missing number: 13 = ?12.
4 — 3 × 4 = 12, so multiply the numerator by 4 as well: 1 × 4 = 4.
Write 1015 in simplest form. (Type your answer like 1/2.)
2/3 — 10 and 15 share a common factor of 5. 10 ÷ 5 = 2 and 15 ÷ 5 = 3, giving 23.
Find the missing number: 56 = 25?.
30 — 5 × 5 = 25, so multiply the denominator by 5 as well: 6 × 5 = 30.
Write 610 as an equivalent fraction with a denominator of 5. (Type your answer like 1/2.)
3/5 — 10 ÷ 2 = 5, so divide the numerator by 2 as well: 6 ÷ 2 = 3. The answer is 35.
Watch out for
- Adding the same number to the numerator and denominator, for example thinking 12 = 23. Use folded paper strips to show that 23 covers more than 12.
- Believing that a fraction with bigger numbers is a bigger amount, such as thinking 48 is more than 12. Shade both on identical strips to compare.
- Changing only the denominator, for example writing 34 = 38. Remind the learner that whatever is done to the bottom must also be done to the top.
Tips for parents
- Start with hands-on folding before moving to numbers. Seeing the same shaded amount helps the rule make sense.
- Use food: cut a sandwich into halves, then quarters, and ask whether the amount eaten has changed.
- When the learner simplifies, ask “Can both numbers still be divided by the same number?” until the answer is no.
Go further
- Make a fraction wall from paper strips showing halves, thirds, quarters, sixths, eighths and twelfths, then list every set of equivalent fractions you can find.
- Play an equivalent-fraction matching game: write fractions on cards, shuffle them and find pairs that are equivalent, such as 23 and 69.
- Investigate: how many fractions equivalent to 34 can you find with a denominator less than 50?