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 be able to:

• Recognise that fractions like 1/2 and 2/4 are the same size
• Use visual models like fraction bars and number lines to show equivalent fractions
• Create new equivalent fractions by multiplying or dividing both the numerator and denominator by the same number
• Find equivalent fractions in everyday situations like sharing pizza or dividing a cake

Why this matters

Equivalent fractions help you understand that different-looking fractions can actually be the same. This is useful when you need to compare fractions, add them together, or simplify them. You use equivalent fractions every day when you share food, divide a cake, or play games with friends. It's like having the same amount of chocolate but in different-sized pieces!

How it works

Let's think of fractions like pieces of a pizza. If you have a pizza cut into 2 equal pieces and you eat 1 piece, you've eaten 1/2 of the pizza. But if the same pizza was cut into 4 equal pieces and you eat 2 pieces, you've still eaten the same amount – 2/4 of the pizza. These are equivalent fractions because they show the same part of the whole.

Here are the steps to find equivalent fractions:

1. Start with a fraction, like 1/2
2. Multiply both the top (numerator) and bottom (denominator) by the same number
3. If you multiply 1 by 2 and 2 by 2, you get 2/4
4. Draw or imagine the same amount of the whole in different ways

You can also divide both numbers by the same number to find equivalent fractions. For example, if you start with 6/12, you can divide both by 6 to get 1/2.

Examples you can see

Let's look at some examples using fraction bars:

Here's how to make equivalent fractions using multiplication:

• Start with 3/5
• Multiply both numbers by 2: 3 × 2 = 6 and 5 × 2 = 10
• So 3/5 = 6/10

And here's how to find equivalent fractions using division:

• Start with 8/12
• Divide both numbers by 4: 8 ÷ 4 = 2 and 12 ÷ 4 = 3
• So 8/12 = 2/3

You can also use number lines to see equivalent fractions:

On a number line from 0 to 1:

• 1/2 is halfway
• 2/4 is also halfway
• 3/6 is also halfway

All these fractions land on the same point, so they are equivalent.

Try it as a mini adventure

Adventure: The Fraction Bakery

You are the head baker at a magical bakery where all cakes are divided into different numbers of pieces. You need to make sure that customers get the same amount of cake, no matter how it's cut!

Task 1: You have a cake cut into 3 pieces. You eat 1 piece. What fraction have you eaten?

Task 2: Now you have another cake cut into 6 pieces. How many pieces should you eat to get the same amount?

Task 3: You want to share 4 pieces of a cake that was cut into 8 pieces with your friend. What fraction of the cake did you eat?

Task 4: If you eat 2 pieces from a cake cut into 10 pieces, what fraction have you eaten? Can you write an equivalent fraction?

Use drawings or real cake pieces to solve these problems. Remember, equivalent fractions show the same amount!

Common mistakes

• Mistake: Only multiply or divide one number in the fraction, like 2/3 = 4/3
• Why it happens: Children might think they only need to change one number to make equivalent fractions
• Fix: Always multiply or divide both top and bottom by the same number

• Mistake: Thinking 1/2 = 2/3 because 1 + 1 = 2 and 2 + 1 = 3
• Why it happens: Mixing up fraction operations with addition
• Fix: Remember that adding numbers in a fraction doesn't make equivalent fractions

• Mistake: Using different numbers to multiply or divide the top and bottom
• Why it happens: Confusion about what "equivalent" means
• Fix: Always use the same number for both numerator and denominator

Parent and carer guide

Equivalent fractions can be tricky, but you can help your child by:

• Using real food like pizza or cake to show the same amount in different ways
• Playing with fraction strips or fraction circles to see how pieces match
• Encouraging them to draw fraction models when solving problems
• Practising with simple multiplication facts like 2 × 2 = 4 to help with finding equivalents
• Noticing when they make mistakes and gently guiding them back to the correct method

Remember: It's okay if they don't get it right away. Equivalent fractions are a big idea that takes time to understand. Keep it fun and practical!

Practice questions

1. What fraction is equivalent to 1/3? Multiply both numbers by 2.
2. Find an equivalent fraction to 4/8 by dividing both numbers by 4.
3. Are 2/5 and 4/10 equivalent? Explain your answer.
4. Write 3/4 as an equivalent fraction with a denominator of 12.
5. What fraction is equivalent to 6/9 when simplified?

Answers:

1. 2/6
2. 1/2
3. Yes, because 2 × 2 = 4 and 5 × 2 = 10
4. 9/12
5. 2/3

FAQ

What are equivalent fractions?

Equivalent fractions are fractions that look different but show the same amount or part of a whole.

How do I find equivalent fractions?

You can find equivalent fractions by multiplying or dividing both the top and bottom numbers by the same number.

Why do we need equivalent fractions?

Equivalent fractions help us compare fractions, add fractions, and simplify them. They show us that different-looking fractions can be the same.

Can you give me a real-life example?

Yes! If you eat 1 slice from a pizza cut into 2 pieces, you eat 1/2 of the pizza. If the same pizza was cut into 4 pieces and you eat 2 slices, you still eat 2/4 of the pizza – that's the same amount!

How can I help my child learn equivalent fractions?

Use everyday examples like sharing food, draw fraction models, play fraction games, and practice with simple multiplication and division facts.