fractions
Comparing fractions with different denominators
Use models, benchmarks and common denominators.
Quick answer
To compare fractions with different denominators, you can use visual models, benchmarks like half or one whole, or find a common denominator so the fractions have the same bottom number.Learning outcome
By the end of this page, you will be able to compare two fractions that have different numbers on the bottom (denominators) and say which one is bigger or smaller. Success signs:- You can draw pictures to show which fraction is bigger
- You can use the word "half" or "whole" to help you decide
- You can find a way to make the bottom numbers the same
- You can explain why one fraction is bigger than the other
Why this matters
Comparing fractions is useful in everyday life when you need to decide which part is bigger or smaller. For example, if you're sharing a pizza with friends, you need to know if one-third of the pizza is more or less than one-half. It's also helpful when you're cooking and need to know if three-quarters of a cup of flour is more than two-thirds of a cup. In school, this skill helps you understand how fractions work and prepares you for more complex maths later on.How it works
There are three main ways to compare fractions with different denominators:- Using visual models – Draw pictures or use objects to see which fraction is bigger
- Using benchmarks – Compare each fraction to half or one whole
- Using common denominators – Make the bottom numbers the same, then compare the top numbers
Examples you can see
Method 1: Visual models Imagine you have two pizzas. One pizza is cut into 4 equal slices and you eat 1 slice. The other pizza is cut into 8 equal slices and you eat 3 slices. Which pizza did you eat more of? You can draw two circles (pizzas). Divide one into 4 parts and shade 1 part. Divide the other into 8 parts and shade 3 parts. Looking at the pictures, you can see that 3 out of 8 is more than 1 out of 4. So, 3/8 > 1/4. Method 2: Using benchmarks Let’s compare 2/5 and 3/8. Think about half: - Is 2/5 more or less than half? - Half of 5 is 2.5, so 2/5 is less than half. - Is 3/8 more or less than half? - Half of 8 is 4, so 3/8 is less than half. Since both are less than half, we need to compare more carefully. But if one was more than half and the other less, you'd know which is bigger. Method 3: Common denominators To compare 2/3 and 3/4: 1. Find a number that both 3 and 4 can go into (a common multiple). - 3 and 4 go into 12. 2. Change both fractions so they have denominator 12: - 2/3 becomes 8/12 (multiply top and bottom by 4) - 3/4 becomes 9/12 (multiply top and bottom by 3) 3. Now compare 8/12 and 9/12. - Since 9 is more than 8, 3/4 is bigger than 2/3.Try it as a mini adventure
Adventure: The Fraction Feast! You are the chef for a party and need to make sure everyone gets the biggest piece of cake. You have two cakes, each cut differently. Cake 1 is cut into 6 equal pieces. You take 2 pieces. Cake 2 is cut into 8 equal pieces. You take 3 pieces. Which cake piece did you get more of? Step-by-step: 1st time: Draw two circles for the cakes. 2nd time: Cut one into 6 pieces and shade 2 pieces. 3rd time: Cut the other into 8 pieces and shade 3 pieces. 4th time: Use the benchmark of half to help decide. 5th time: Change both fractions to have the same bottom number. 6th time: Compare the top numbers. You find that 3/8 is more than 2/6, so you got more cake from Cake 2!Common mistakes
- Mistake: Thinking that the bigger number on top means the fraction is bigger. Why it happens: Children sometimes forget that the bottom number shows how many pieces the whole is cut into. Fix: Always think about the size of each piece. If the whole is cut into 8 pieces, each piece is smaller than if it's cut into 4 pieces.
- Mistake: Adding fractions instead of comparing them. Why it happens: Children mix up the operations they've learned. Fix: Remember, comparing means "which one is bigger", not "what do they make together?"
- Mistake: Not using visual models when starting out. Why it happens: It can be hard to think about fractions without seeing them. Fix: Always draw pictures or use real objects like pizza slices or blocks to help you understand.
Parent and carer guide
Parents and carers can help by:- Using everyday examples like pizza, cake, or chocolate bars to explain fractions
- Letting children draw pictures of fractions to understand the concept
- Practising with simple fractions first, like halves, quarters, and thirds
- Encouraging children to use the word "half" as a helpful benchmark
- Being patient when children make mistakes – it's part of learning
Practice questions
- Which is bigger: 1/3 or 1/4?
- Compare 2/5 and 3/10.
- Which is larger: 3/6 or 2/3?
- Is 4/8 greater than, less than, or equal to 1/2?
- Which fraction is bigger: 5/7 or 3/5?
- 1/3 is bigger because when you draw it, 1 out of 3 pieces is larger than 1 out of 4 pieces.
- 2/5 is bigger. Change to 4/10 and 3/10.
- 2/3 is bigger. Change to 6/6 and 3/6.
- They are equal. 4/8 is the same as 1/2.
- 5/7 is bigger. Change to 25/35 and 21/35.
FAQ
How do I know which fraction is bigger when the denominators are different?
You can use visual models, compare to half, or change the fractions so they have the same bottom number (common denominator).
Why do we need to find a common denominator?
It's easier to compare fractions when they have the same bottom number. It's like comparing apples to apples – they're the same size so you can see which one is bigger.
Can I use a calculator to compare fractions?
Yes, you can, but it's good to understand how to do it without a calculator first. This helps you understand what you're doing.
What if I can't find a common denominator easily?
You can always draw pictures or use benchmarks like half to help you decide.
Are all fractions with the same numerator the same?
No. For example, 1/2 is bigger than 1/4 because the whole is cut into fewer pieces.