X Tables
Ratio Proportion

Ratio misconceptions

Fix errors such as adding the same amount instead of multiplying by the same factor.

Quick answer

Ratio misconceptions happen when children think that if you add the same amount to both parts of a ratio, the ratio stays the same. This is wrong – you must multiply or divide both parts by the same amount to keep the ratio the same.

Learning outcome

By the end of this page, you will understand how to keep ratios the same when changing them, and you'll know why adding the same amount doesn’t work. Success signs:
  • You can explain why adding the same number to both parts of a ratio changes it
  • You can find equivalent ratios by multiplying both parts by the same number
  • You can spot when someone has made a ratio mistake
  • You can solve simple ratio problems using correct methods

Why this matters

Understanding ratios helps you solve many real-life problems. Whether you're sharing snacks, mixing paint, cooking recipes, or playing games, ratios help you keep things fair and balanced. When you get ratios wrong, things can go wrong too – like making soup too salty or sharing cookies unfairly. Learning to handle ratios correctly helps you make better decisions in everyday life and in maths class.

How it works

A ratio shows how two amounts compare. For example, if you have 2 red sweets and 3 blue sweets, the ratio is 2:3. This means for every 2 red sweets, there are 3 blue sweets. To keep a ratio the same, you must multiply or divide both parts by the same number. This is called making an equivalent ratio. Let’s break it down step by step:
  1. Start with a ratio, like 2:3
  2. Multiply both parts by the same number, for example 2
  3. 2 × 2 = 4 and 3 × 2 = 6
  4. The new ratio is 4:6, which is the same as 2:3
If you add the same number instead of multiplying, the ratio changes:
  • 2 + 1 = 3 and 3 + 1 = 4
  • New ratio is 3:4 – this is different from 2:3!

Examples you can see

Let’s look at some fun examples that help you understand ratios better. Example 1: Sharing cookies You and your friend want to share 10 cookies so that you get 2 and your friend gets 3. That’s the ratio 2:3. If you double the number of cookies, you have 20 cookies. To keep the same sharing, you must double both parts:
  • 2 × 2 = 4 (you get 4 cookies)
  • 3 × 2 = 6 (your friend gets 6 cookies)
So the new ratio is 4:6, which is the same as 2:3. Example 2: Mixing paint To make purple paint, you mix 2 parts blue with 3 parts red. That’s the ratio 2:3. If you want to make more purple paint, you can use 4 parts blue and 6 parts red – that’s still 2:3 because both parts were doubled. Example 3: Building blocks You build a tower with 3 red blocks and 5 blue blocks. That’s the ratio 3:5. If you double the tower, you use 6 red blocks and 10 blue blocks. The ratio is still 3:5 because both parts were multiplied by 2.

Try it as a mini adventure

Adventure: The Magic Ratio Quest You are on a quest to find the secret of the Magic Ratio! You must solve a puzzle to get the key.
  1. First, you find a chest with 4 gold coins and 6 silver coins. The ratio is 4:6.
  2. You must make a new chest with the same ratio, but with 8 gold coins.
  3. How many silver coins do you need?
To solve this, you must multiply both parts of the ratio by the same number to keep it the same.
  • 4 × 2 = 8 (gold coins)
  • 6 × 2 = 12 (silver coins)
So you need 12 silver coins to keep the ratio 4:6 the same. The new ratio is 8:12 – that’s the same as 4:6! Try this again with other numbers:
  • Original ratio: 3:7
  • You want 6 gold coins
  • How many silver coins do you need?
  1. 3 × 2 = 6
  2. 7 × 2 = 14
So the new ratio is 6:14, which is the same as 3:7.

Common mistakes

Here are some mistakes children often make with ratios and how to fix them: Mistake 1: Adding the same number to both parts of a ratio.
  • Incorrect: 2:3 becomes 3:4 by adding 1 to both parts
  • Why it happens: Children think that if you change both numbers the same way, it’s the same ratio
  • Fix: Always multiply or divide both parts by the same number
Mistake 2: Thinking that 2:3 and 4:6 are different.
  • Incorrect: 2:3 and 4:6 are not the same ratio
  • Why it happens: Children don’t understand that 4:6 is just 2:3 doubled
  • Fix: Show that 4 ÷ 2 = 2 and 6 ÷ 2 = 3 – so they are the same ratio
Mistake 3: Mixing up which number is which in a ratio.
  • Incorrect: If the ratio is 5:3, children might say it’s 3:5
  • Why it happens: Children don’t read the ratio carefully
  • Fix: Always read the ratio in order and use objects or drawings to help

Parent and carer guide

Parents and carers can help by:
  • Using real-life examples like sharing snacks or mixing paint
  • Practising with small numbers first, then increasing the difficulty
  • Encouraging children to explain their thinking
  • Using visual aids like drawings or blocks to show ratios
  • Playing games that involve ratios, like making equal groups or sharing items
What to say:
  • “Let’s see if we can make the same ratio with more items.”
  • “Can you show me how you know 2:3 and 4:6 are the same?”
  • “What happens if we add the same number to both parts?”
What not to worry about:
  • It’s normal for children to make mistakes at first
  • Don’t rush – take time to explain and practice
  • Focus on understanding, not just getting the right answer

Practice questions

  1. What is the equivalent ratio to 3:5 if you multiply both parts by 2?
  2. Which ratio is the same as 4:7? (Choose from: 8:14, 12:21, 16:28)
  3. Start with the ratio 1:4. What is the equivalent ratio if you multiply both parts by 3?
  4. Original ratio is 6:9. What is the equivalent ratio if you divide both parts by 3?
  5. Is 2:3 the same as 6:9? Why or why not?
Answers:
  1. 6:10
  2. 8:14
  3. 3:12
  4. 2:3
  5. Yes, because 6 ÷ 3 = 2 and 9 ÷ 3 = 3

FAQ

What is a ratio?

A ratio compares two amounts. For example, if you have 3 red sweets and 2 blue sweets, the ratio is 3:2.

Why do I need to multiply both parts of a ratio?

Because multiplying keeps the relationship between the two amounts the same. Adding changes the relationship.

Can I use subtraction to make equivalent ratios?

No, you must multiply or divide both parts by the same number to keep the ratio the same.

What does “equivalent ratio” mean?

It means two ratios that show the same relationship, like 2:3 and 4:6.

How can I check if two ratios are the same?

Divide both parts of one ratio by the same number to see if you get the other ratio.