Age Guides
Age 9 guide to equivalent fractions
Age-appropriate activities, explanations and practice ideas for equivalent fractions.
Quick answer
Equivalent fractions are different fractions that show the same amount. You can find them by multiplying or dividing both the top and bottom numbers by the same number.Learning outcome
By the end of this page, you will understand how to make equivalent fractions and recognise when two fractions are the same, even if they look different. Success signs:- You can draw or show how two fractions are the same
- You can multiply or divide both the top and bottom numbers by the same number to make an equivalent fraction
- You can match fractions that are equivalent
- You can explain why 1/2 is the same as 2/4
Why this matters
Equivalent fractions help you understand that fractions can look different but still be the same size. This is useful when comparing fractions, adding fractions, and solving problems in real life. For example, when sharing a pizza or dividing a cake, you might need to know that half a pizza is the same as two quarters of the same pizza.How it works
To find equivalent fractions, you multiply or divide both the top (numerator) and bottom (denominator) numbers by the same number. This keeps the fraction the same size, just with different numbers. Let's start with a simple example:- Start with the fraction 1/2
- Multiply both numbers by 2: 1 × 2 = 2 and 2 × 2 = 4
- This gives us 2/4
- 1/2 and 2/4 are equivalent fractions
- Start with 6/8
- Divide both numbers by 2: 6 ÷ 2 = 3 and 8 ÷ 2 = 4
- This gives us 3/4
- 6/8 and 3/4 are equivalent fractions
Examples you can see
Here are some examples of equivalent fractions using visual models and real-world situations. Example 1: Pizza sharing Imagine you have a pizza cut into 4 equal slices. You eat 2 slices. That's 2/4 of the pizza. Now imagine the same pizza cut into 8 equal slices. You eat 4 slices. That's 4/8 of the pizza. Both 2/4 and 4/8 show the same amount of pizza. They are equivalent fractions. Example 2: Drawing fractions Draw a rectangle and split it into 3 equal parts. Shade 2 parts. This shows 2/3. Now draw another rectangle of the same size and split it into 6 equal parts. Shade 4 parts. This shows 4/6. Both rectangles show the same amount shaded. So 2/3 = 4/6. Example 3: Using multiplication If you have 3/5 and want to find an equivalent fraction:- Multiply both numbers by 2: 3 × 2 = 6 and 5 × 2 = 10
- So 3/5 = 6/10
- Divide both numbers by 5: 10 ÷ 5 = 2 and 15 ÷ 5 = 3
- So 10/15 = 2/3
Try it as a mini adventure
The Fraction Explorer's Quest You are a fraction explorer on a mission to find treasure. You must solve fraction puzzles to unlock the treasure chest. Step 1: You see a fraction on the map: 1/2. To find the first clue, you need to find an equivalent fraction. What is 1/2 × 2? Step 2: The next clue says "Find the fraction that equals 3/4 by dividing both numbers by 1". What is 3/4 ÷ 1? Step 3: You see a fraction: 4/8. What fraction is equivalent to this when you multiply both numbers by 3? Step 4: The final puzzle says "Simplify 12/18 to find the treasure key". What is 12/18 ÷ 6? Step 5: You have collected all the clues. What fraction is equivalent to 1/3 when you multiply both numbers by 4? Answer Key:- 1/2 × 2 = 2/4
- 3/4 ÷ 1 = 3/4
- 4/8 × 3 = 12/24
- 12/18 ÷ 6 = 2/3
- 1/3 × 4 = 4/12
Common mistakes
- Mistake: Only multiplying or dividing one number in the fraction
Why it happens: Children might think they can change just the top or bottom number
Fix: Always multiply or divide both the top and bottom by the same number - Mistake: Thinking that 2/4 is not the same as 1/2
Why it happens: Children might not see that 2/4 is just 1/2 shown differently
Fix: Use drawings or real objects to show that 2/4 and 1/2 are the same amount - Mistake: Not finding the right number to multiply or divide by
Why it happens: Children might not know multiplication facts well
Fix: Practice multiplication tables and look for common factors
Parent and carer guide
Parents and carers can help children understand equivalent fractions by:- Using visual aids like fraction circles, bars, or pizzas
- Practising with everyday examples like sharing food or dividing a cake
- Playing fraction games using cards or online activities
- Encouraging children to draw pictures of fractions to show equivalence
- Checking that children multiply or divide both top and bottom numbers by the same amount
- Use concrete materials like counters or blocks to show equal groups
- Start with simple fractions like 1/2 and 2/4
- Reinforce that equivalent fractions represent the same amount
- Be patient and celebrate small successes
Practice questions
- What fraction is equivalent to 2/3 when you multiply both numbers by 3?
- Find an equivalent fraction to 4/8 by dividing both numbers by 4.
- Which fraction is the same as 3/6? (Choose from: 1/2, 1/3, 2/3)
- What fraction is equivalent to 5/10 when you multiply both numbers by 2?
- What is 6/9 simplified by dividing both numbers by 3?
- 2/3 × 3 = 6/9
- 4/8 ÷ 4 = 1/2
- 1/2
- 5/10 × 2 = 10/20
- 6/9 ÷ 3 = 2/3
FAQ
What are equivalent fractions?
Equivalent fractions are different fractions that show the same amount or part of a whole.
How do I know if two fractions are equivalent?
You can check by multiplying or dividing both the top and bottom numbers of one fraction by the same number to get the other fraction.
Can I make equivalent fractions by adding or subtracting?
No, you can only make equivalent fractions by multiplying or dividing both numbers by the same number.
Why do we need equivalent fractions?
Equivalent fractions help us compare fractions, add fractions, and solve problems where fractions look different but represent the same amount.
How can I practice equivalent fractions at home?
You can use fraction circles, draw pictures, use food like pizza or cake to share, or play online fraction games to practice.