Ratio compares two quantities — like ingredients in a recipe or colours in a pattern. Proportion tells us how things scale. Master these and you'll unlock real-world maths: cooking, maps, mixing paint, and splitting money!
🔢 Simplifying Ratios
12 : 8 ÷4 3 : 2 (HCF = 4)
🍕 Dividing in a Ratio
Share £40 in 3:5 → 8 parts total, each part = £5 → £15 : £25
Ratio notation: We write ratios using a colon, e.g., 3:2 means "3 for every 2". Order matters — 3:2 is NOT the same as 2:3.
Simplifying ratios: Divide both numbers by their Highest Common Factor (HCF), just like simplifying a fraction. E.g., 10:15 → HCF is 5 → 2:3.
Dividing in a ratio (3 steps): Add the parts to find the total number of shares. Divide the quantity by the total shares to find one share. Multiply each part of the ratio by one share.
Direct proportion: If two quantities are in direct proportion, when one doubles the other doubles too. Use the "unitary method": find the value of ONE unit first, then scale up.
Scaling recipes: Identify the scale factor (new quantity ÷ original quantity), then multiply ALL ingredients by it.
Check: When dividing in a ratio, make sure your two answers add back up to the original amount!
📝 Worked Examples
Study each method carefully — then try the drag exercises!
Example 1: Simplifying a Ratio
Question: Simplify the ratio 18:24.
Step 1: Find the HCF of 18 and 24. Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. HCF = 6.
Step 2: Divide both parts by the HCF. 18 ÷ 6 = 3. 24 ÷ 6 = 4.
Step 3: Simplified ratio = 3:4.
Check: 3 and 4 share no common factors other than 1 — fully simplified! ✓
Example 2: Dividing a Quantity in a Ratio
Question: Share £56 between Ali and Ben in the ratio 3:4.
Step 1: Add the parts. 3 + 4 = 7 parts total.
Step 2: Find one part. £56 ÷ 7 = £8 per part.
Step 3: Multiply each person's share. Ali = 3 × £8 = £24. Ben = 4 × £8 = £32.
Check: £24 + £32 = £56 ✓
Example 3: Direct Proportion (Unitary Method)
Question: 5 notebooks cost £6.25. How much do 8 notebooks cost?
Step 1: Find the cost of 1 notebook. £6.25 ÷ 5 = £1.25 per notebook.
Step 2: Multiply by the new quantity. 8 × £1.25 = £10.00.
Answer: 8 notebooks cost £10.00.
Example 4: Scaling a Recipe
Question: A cake recipe for 6 people needs 300g flour, 150g sugar, and 4 eggs. Scale it up for 15 people.
Step 1: Find the scale factor. 15 ÷ 6 = 2.5.
Step 2: Multiply all ingredients by 2.5.
Flour: 300g × 2.5 = 750g
Sugar: 150g × 2.5 = 375g
Eggs: 4 × 2.5 = 10 eggs
Answer: 750g flour, 375g sugar, 10 eggs.
🔬 Ratio Splitter
Enter a total amount and a ratio (A:B). See the quantity split visually and calculate each share!
split in
:
🎯 Drag 1: Simplify the Ratio
The ratio of red to blue marbles is 6 : 4. Drag the correct simplified ratio into the box.
3:2
2:3
6:4
1:2
6 : 4 =
?
Hint: Find the HCF of 6 and 4, then divide both parts by it.
🎯 Drag 2: Simplify the Ratio
A drink is made with 15ml orange juice and 25ml lemonade. Write the ratio in its simplest form.
3:5
5:3
1:5
15:25
15 : 25 =
?
Hint: What is the HCF of 15 and 25?
🎯 Drag 3: Share in a Ratio
Share 30 sweets between Ava and Ben in the ratio 2 : 3. Drag the correct amount for Ava (Part A) and Ben (Part B).
12
18
15
10
Ava:
?
Ben:
?
Hint: 2+3=5 parts. 30 ÷ 5 = one share. Then multiply!
🎯 Drag 4: Share Money in a Ratio
Ali and Ben share £56 in the ratio 3 : 4. Drag the correct amounts for Ali (Part A) and Ben (Part B).
£24
£32
£21
£28
Ali:
?
Ben:
?
Hint: 3+4=7 parts. £56 ÷ 7 = one share.
🎯 Drag 5: Direct Proportion
4 pens cost £2.00. How much do 7 pens cost? Drag the correct answer.
£3.50
£3.00
£4.00
£2.50
7 pens cost
?
Hint: Find the cost of 1 pen first (unitary method).
🎯 Drag 6: Scaling a Recipe
A biscuit recipe for 4 people uses 200g of flour. How much flour is needed for 10 people?
500g
400g
600g
250g
For 10 people:
?
Hint: Scale factor = 10 ÷ 4. Then multiply the flour.
✏️ Practice Questions
Simplify the ratio 4:6.
Simplify the ratio 12:18.
Simplify the ratio 20:35.
Simplify the ratio 16:40.
Write the ratio of shaded to unshaded squares if there are 9 shaded and 6 unshaded. Simplify your answer.
Share 20 sweets between two children in the ratio 3:2. How many does each child get?
Share £45 in the ratio 2:7. What is each share?
Share 72kg in the ratio 5:4. What is each share?
Three friends share a pizza in the ratio 1:2:3. If the pizza is cut into 12 slices, how many slices does each person get?
A paint colour is made from red and white in the ratio 3:5. How much red paint is needed if you use 40ml of white paint?
If 3 apples cost 90p, how much do 7 apples cost?
A car travels 150km in 3 hours. How far does it travel in 5 hours at the same speed?
6 pencils cost £1.80. How much do 9 pencils cost?
A recipe for 4 people needs 320g of pasta. How much pasta is needed for 7 people?
A model car is built to a scale of 1:25. If the model is 16cm long, how long is the real car? Give your answer in metres.
Are 4 and 10 in the same ratio as 6 and 15? Explain how you know.
A school has 360 students. The ratio of boys to girls is 7:5. How many girls are in the school?
Sam mixes squash and water in the ratio 1:4. How much squash does he need to make 750ml of drink?
A map has a scale of 1:50 000. Two towns are 8cm apart on the map. What is the real distance in kilometres?
The angles in a triangle are in the ratio 2:3:4. What is the size of each angle? (Hint: angles in a triangle add up to 180°.)
Answers:
2:3
2:3
4:7
2:5
3:2
12 sweets : 8 sweets
£10 : £35
40kg : 32kg
2 slices : 4 slices : 6 slices
24ml red paint (ratio 3:5 means 5 parts=40ml, 1 part=8ml, 3 parts=24ml)
£2.10 (1 apple = 30p, 7 × 30p = £2.10)
250km (50km/h, 5 × 50 = 250)
£2.70 (1 pencil = 30p, 9 × 30p = £2.70)
560g (per person = 80g, 7 × 80 = 560)
4m (16 × 25 = 400cm = 4m)
Yes — 4:10 = 2:5 and 6:15 = 2:5 (both simplify to 2:5)
150 girls (5 parts of 360 ÷ 12 = 30, 5 × 30 = 150)
A bakery makes chocolate and vanilla cupcakes in the ratio 5:3. They bake 120 cupcakes in total. How many of each flavour do they make?
A juice drink is made from apple, orange and mango in the ratio 3:2:1. A bottle contains 600ml. How many millilitres of each juice are there?
Emily earns £120 for working 8 hours. How much does she earn for working 11 hours at the same rate?
A farmer plants carrots and potatoes in the ratio 4:5. He plants 360 vegetable plants in total. How many more potato plants than carrot plants does he plant?
A map is drawn to a scale of 1:200 000. The distance between two cities on the map is 6.5cm. What is the actual distance between the cities? Give your answer in kilometres.
Gold is mixed with silver in the ratio 2:9 by mass to make a piece of jewellery weighing 88g. How many grams of gold and how many grams of silver are used?
A swimming pool is filled at a rate of 2500 litres every 4 hours. At this rate, how long will it take to fill the pool if it holds 15 000 litres? Give your answer in hours.
Tom and Jerry share some money in the ratio 7:3. Tom gets £42 more than Jerry. How much money did they share altogether?
The ratio of cats to dogs at an animal shelter is 3:4. If there are 84 animals in total, how many more dogs than cats are there?
A recipe for 8 portions of soup requires 400g carrots, 300g onions and 1.2 litres of stock. Adjust the recipe for 14 portions. Give each ingredient to the nearest gram (or ml).