Write the ratio of 6 apples to 3 oranges.
Write apples first, then oranges.
The ratio is written in order: apples : oranges → 6 : 3.
Ratio Introduction
Ratios are used to compare quantities and show how values relate to each other. Understanding ratio notation is essential for solving problems involving direct proportion and scaling in GCSE Maths.
Overview
A ratio compares one amount with another amount.
It tells you how many parts there are of each thing.
Red : Blue = \( 2 : 3 \)
This means for every 2 red parts, there are 3 blue parts.
Ratio does not tell you the exact total straight away — it tells you the relationship.
What you should understand after this topic
- Understand what ratio means
- Write a ratio using \( : \)
- Simplify a ratio
- Find total parts in a ratio
- Use a ratio to share an amount
Key Definitions
Ratio
A comparison between amounts.
Part
One section of a ratio.
Simplify
Write the ratio in its smallest whole-number form.
Equivalent Ratio
A ratio with the same value, written in a different way.
Total Parts
The sum of all the numbers in the ratio.
Share in a Ratio
Split a total amount according to the number of parts.
Key Rules
Order matters
\( 2:3 \) is not the same as \( 3:2 \).
Use the same units
Convert first if needed before writing a ratio.
Simplify fully
Divide both parts by the highest common factor.
Add parts for the total
For \( 2:3 \), the total number of parts is \( 5 \).
How to Solve
Step 1: Understand ratio
A ratio compares amounts. It shows how many parts of one thing there are compared with another.
\( 3:5 \)
This means 3 parts to 5 parts.
Exam tip: Ratio is not the same as a fraction.
Step 2: Write ratios correctly
Write the ratio in the same order as the words in the question.
Apples : Oranges = \( 4:6 \)
Order matters — changing the order changes the meaning.
Step 3: Simplify ratios
Simplify by dividing both parts by the same number.
\( 4:6 = 2:3 \)
Use the highest common factor (HCF) from factors and multiples.
Exam thinking: Always give ratios in simplest form unless told otherwise.
Step 4: Use equivalent ratios
\( 2:3 = 4:6 = 6:9 \)
Multiply or divide both parts by the same number.
Step 5: Share amounts using ratios
Example idea: This method works for all sharing questions.
- Add the parts of the ratio.
- Divide the total by this number.
- Multiply each part by the value of one part.
Step 6: Check units before forming ratios
Convert all values to the same unit first using units and conversions.
Exam tip: Mixed units is a very common mistake.
Step 7: Exam method summary
See direct proportion and inverse proportion for advanced ratio problems.
- Write the ratio in the correct order.
- Simplify if needed.
- Add parts for sharing questions.
- Divide and multiply to find each share.
- Check units are consistent.
Example Questions
Edexcel
Exam-style questions inspired by Edexcel GCSE Mathematics, focusing on writing, simplifying, and interpreting ratios.
Edexcel
Write the ratio of 12 to 18 in its simplest form.
Edexcel
Simplify the ratio \( 20:35 \).
Edexcel
Write the ratio 5 m to 200 cm in its simplest form.
Edexcel
In a class, there are 14 boys and 21 girls. Write the ratio of boys to girls in its simplest form.
Edexcel
Write the ratio of red counters to blue counters in its simplest form.
AQA
Exam-style questions based on the AQA GCSE Mathematics specification, focusing on interpreting and forming ratios from diagrams and real-life contexts.
AQA
Write the ratio \( 24:36 \) in its simplest form.
AQA
There are 8 apples and 12 oranges in a basket. Write the ratio of apples to oranges in its simplest form.
AQA
Divide both parts of the ratio \( 45:60 \) by their highest common factor.
AQA
Write the ratio of shaded squares to unshaded squares in its simplest form.
AQA
A drink is made using 2 parts juice and 3 parts water. Write the ratio of juice to water.
OCR
Exam-style questions aligned with OCR GCSE Mathematics, emphasising reasoning, unit consistency, and visual interpretation.
OCR
Simplify the ratio \( 18:27 \).
OCR
Write the ratio of 2 hours to 30 minutes in its simplest form.
OCR
Write the ratio of green beads to yellow beads in its simplest form.
OCR
Write the ratio of £3 to 75 pence in its simplest form.
OCR
Explain why ratios must be written using quantities in the same units.
Exam Checklist
Step 1
Read the order carefully.
Step 2
Check the units match before writing the ratio.
Step 3
Simplify fully using the highest common factor.
Step 4
For sharing questions, find total parts first.
Most common exam mistakes
Order mistake
Writing boys:girls when the question asks for girls:boys.
Unit mistake
Comparing cm with mm without converting.
Part mistake
Using one ratio number instead of the total number of parts.
Simplifying mistake
Stopping too early and not reducing to simplest form.
Common Mistakes
These are common mistakes students make when working with ratios in GCSE Maths.
Writing the ratio in the wrong order
Incorrect
A student reverses the order of the quantities.
Correct
Follow the order given in the question. For example, if it says boys : girls, the ratio must match that order.
Not simplifying fully
Incorrect
A student leaves the ratio unsimplified.
Correct
Divide all parts of the ratio by their highest common factor to write it in simplest form.
Adding parts incorrectly
Incorrect
A student makes an error when adding the parts of the ratio.
Correct
Add all parts carefully. The total number of parts is needed when sharing or finding values.
Sharing without finding one part
Incorrect
A student tries to split a quantity directly using the ratio.
Correct
First find the value of one part by dividing the total by the number of parts, then multiply to find each share.
Comparing different units
Incorrect
A student compares quantities without converting units.
Correct
Always convert to the same units before forming or comparing ratios.
Try It Yourself
Practise understanding and simplifying ratios.
Foundation
Foundation Practice
Write and simplify basic ratios.
Simplify the ratio 8 : 4.
Divide both parts by the same number.
Divide both by 4 → 2 : 1.
Write the ratio of 10 boys to 5 girls in simplest form.
Simplify 10 : 5.
10 : 5 simplifies by dividing both by 5 → 2 : 1.
Simplify the ratio 12 : 18.
Find the highest common factor.
Divide both by 6 → 2 : 3.
There are 7 red balls and 3 blue balls. What is the ratio red : blue?
Follow the order: red first.
Red : blue → 7 : 3.
Simplify 15 : 20.
Divide both by 5.
15 : 20 → divide by 5 → 3 : 4.
Write the ratio 9 cm to 3 cm in simplest form.
Divide both parts by 3.
9 : 3 simplifies to 3 : 1.
Simplify the ratio 20 : 50.
Divide both by 10.
20 : 50 → divide by 10 → 2 : 5.
Which of these is the simplest form of 12 : 8?
Divide both numbers by 4.
12 : 8 → divide by 4 → 3 : 2.
Simplify the ratio 4 hours : 2 hours.
Units are the same, so just simplify.
4 : 2 → divide by 2 → 2 : 1.
Higher
Higher Practice
Simplify ratios involving decimals, fractions and units.
Simplify the ratio 0.6 : 0.2.
Multiply both numbers by 10 first.
0.6 : 0.2 → 6 : 2 → 3 : 1.
Simplify the ratio 2.5 : 1.5.
Multiply both by 2 to remove decimals.
2.5 : 1.5 → 5 : 3.
Simplify the ratio 3/4 : 1/2.
Multiply both parts by 4.
3/4 : 1/2 → multiply by 4 → 3 : 2.
Write the ratio 250 g : 1 kg in simplest form.
Convert kg to grams.
1 kg = 1000 g → 250 : 1000 → 1 : 4.
Simplify the ratio 0.8 : 1.2.
Multiply both by 10 first.
0.8 : 1.2 → 8 : 12 → 2 : 3.
Simplify the ratio 120 : 150.
Divide both by 30.
120 : 150 → divide by 30 → 4 : 5.
Simplify the ratio 0.25 : 0.75.
Multiply both by 100.
0.25 : 0.75 → 25 : 75 → 1 : 3.
Simplify the ratio 45 minutes : 1.5 hours.
Convert hours to minutes.
1.5 hours = 90 minutes → 45 : 90 → 1 : 2.
A student simplifies 0.4 : 0.6 to 4 : 6 and stops. What did they forget?
4 : 6 can still be simplified.
4 : 6 simplifies to 2 : 3. They stopped too early.
Simplify the ratio 5/6 : 10/12.
Convert both fractions to the same denominator.
5/6 = 10/12, so the ratio is 1 : 1.
Games
Practise this topic with interactive games.
Games coming soon.
Ratio Introduction Video Tutorial
Frequently Asked Questions
What is a ratio?
A ratio compares two or more quantities, showing their relative sizes.
How is a ratio written?
Ratios can be written using a colon (e.g., 2:3), as a fraction (2/3), or in words such as '2 to 3'.
What does the ratio 2:3 mean?
It means that for every 2 parts of the first quantity, there are 3 parts of the second.
How do you simplify a ratio?
Divide all parts of the ratio by their highest common factor (HCF).
Can ratios be simplified like fractions?
Yes, ratios are simplified in the same way as fractions by dividing by a common factor.
Can ratios contain more than two quantities?
Yes, for example 2:3:5 compares three quantities.
What is an equivalent ratio?
An equivalent ratio represents the same relationship, such as 1:2 and 2:4.
Where are ratios used in real life?
Ratios are used in recipes, maps, scale drawings, finance, and probability.