💡 Multiplier = (desired serves) ÷ (original serves). Keep the ratio between ingredients constant!
💡 Worked Examples
Example 1: Simplifying Ratios with Units
Simplify the ratio 45 minutes : 2 hours
Step 1: Convert to the same unit (minutes). 2 hours = 120 minutes.
Step 2: Ratio becomes 45 : 120
Step 3: HCF of 45 and 120 = 15. Divide both by 15.
Answer: 3 : 8
✔ Check: 3 × 15 = 45 ✓ and 8 × 15 = 120 ✓
Example 2: Dividing £120 in Ratio 3 : 5
Share £120 between Alice and Bob in the ratio 3 : 5.
Step 1: Total parts = 3 + 5 = 8
Step 2: Value of 1 part = £120 ÷ 8 = £15
Step 3: Alice = 3 × £15 = £45 · Bob = 5 × £15 = £75
Check: £45 + £75 = £120 ✓
💡 The person with the larger ratio part always gets more.
Example 3: Combining Ratios A:B:C
Given A : B = 2 : 3 and B : C = 4 : 7, find A : B : C.
Step 1: B is 3 in the first ratio and 4 in the second. LCM(3, 4) = 12.
Step 2: Scale A : B = 2 : 3 by ×4 → 8 : 12
Step 3: Scale B : C = 4 : 7 by ×3 → 12 : 21
Answer: A : B : C = 8 : 12 : 21
💡 Could you simplify 8:12:21? HCF = 1, so this is already in simplest form.
Example 4: Map Scale Calculation
A map has scale 1 : 25 000. Two towns are 8 cm apart on the map. How far apart are they in reality? Give your answer in km.
Step 1: Real distance = 8 × 25 000 = 200 000 cm
Step 2: Convert: 200 000 cm ÷ 100 = 2 000 m ÷ 1000 = 2 km
Answer: 2 km
🗺️ Remember: ÷100 to get metres, ÷1000 to get km from metres.
🍰 Visualizer
Ratio Bar Model
Enter a ratio (up to 5 parts) and a total amount, then see the animated bar split!
Recipe Ratio Scaler 🧁
This cupcake recipe serves 4. Drag the slider to scale it up or down!
Serves 2Serves 20
Scaling for 4 serves (×1)
Ingredient
Base (4 serves)
Scaled Amount
Plain flour
200 g
200 g
Unsalted butter
100 g
100 g
Caster sugar
150 g
150 g
Eggs
2
2
Milk (ml)
60 ml
60 ml
Fair Shares Game 🪙
Map Calculator 🗺️
Also calculates the reverse — enter real distance to find map distance:
✏️ Exercise 1: Simplify Ratios
Simplify each ratio to its simplest form. Use the format a:b (no spaces).
✏️ Exercise 2: Divide a Quantity in a Ratio
Find the smaller share in each question. Give a numerical answer only.
✏️ Exercise 3: Find One Part
One share is given — find the other share or the total as asked.
🗺️ Exercise 4: Combining Ratios & Map Scales
Combining ratios and scale problems. Give answers in the units shown.
📝 Exercise 5: Word Problems
Read carefully and identify what is being asked. Numerical answers only.
📝 Practice Questions
Simplify the ratio 14 : 21.
Simplify the ratio 30 : 45 : 60.
Convert and simplify: 400 m : 2 km.
Find the missing value: 3 : 7 = 12 : ?
Share £72 in the ratio 1 : 3.
Share 200 g in the ratio 3 : 7.
Three friends share a prize of £360 in the ratio 2 : 3 : 4. How much does each receive?
Lena and Matt share sweets in ratio 5 : 3. Lena gets 35 sweets. How many does Matt get?
Blue and red paint are mixed in ratio 2 : 5. You have 14 litres of blue. How much red do you need?
A : B = 3 : 4 and B : C = 2 : 5. Find A : B : C.
Scale 1 : 20 000. Map distance = 5 cm. Real distance in km?
Scale 1 : 50 000. Real distance = 4 km. Map distance in cm?
A recipe for 6 biscuits needs 120 g flour. How much for 15 biscuits?
Concrete is made from cement, sand, gravel in ratio 1 : 2 : 4. How much sand is in 140 kg of concrete?
Share £500 in the ratio 3 : 5 : 2. What is the largest share?
A model car has a scale of 1 : 24. The real car is 4.8 m long. How long is the model in cm?
Ali has red to blue beads in ratio 4 : 3. He has 28 red beads. How many beads does he have in total?
A : B = 5 : 2 and B : C = 4 : 3. Find A : B : C in simplest form.
Two jugs hold water in ratio 7 : 3. Together they hold 5 litres. How much is in the larger jug? Give your answer in ml.
A map has scale 1 : 25 000. Two landmarks are 12 cm apart on the map. What is the real distance in km?
2 : 3
2 : 3 : 4
1 : 5
28
£18 and £54
60 g and 140 g
£80, £120, £160
21 sweets
35 litres
A : B : C = 3 : 4 : 10
1 km
8 cm
300 g
40 kg
£250
20 cm
49 beads
A : B : C = 10 : 4 : 3
3500 ml
3 km
🏆 Challenge Questions
Harder ratio problems — show all working!
P and Q share money in ratio 5 : 3. Q's share is £24 less than P's share. How much does each receive?
A school has boys and girls in ratio 7 : 5. There are 48 more boys than girls. How many pupils are there altogether?
Three numbers are in ratio 2 : 5 : 8. The difference between the largest and smallest is 36. Find all three numbers.
A : B = 3 : 5 and A : C = 2 : 7. Find A : B : C.
A map has scale 1 : 40 000. A road appears to be 7.5 cm long on the map. The road is actually measured as 3.2 km on the ground. What is the percentage error in the map reading?
Brass is an alloy of copper and zinc in the ratio 3 : 2. A craftsman has 180 g of copper and 100 g of zinc. What is the maximum mass of brass he can make? How much of each metal is left over?
A recipe for 8 people needs eggs and flour in ratio 1 : 3 by mass. Flour costs £1.20 per 500 g and eggs weigh 60 g each and cost 25p each. For 20 people, calculate the total cost of these two ingredients.
On a scale drawing, a room measures 6 cm by 4.5 cm. The scale is 1 : 200. Calculate the actual area of the room in m².
P = £60, Q = £36. (Difference = 2 parts = £24 → 1 part = £12. P = 5×12 = £60, Q = 3×12 = £36)
288 pupils. (Difference = 2 parts = 48 → 1 part = 24. Total = 12 × 24 = 288)
12, 30, 48. (Difference = 6 parts = 36 → 1 part = 6. Numbers: 2×6=12, 5×6=30, 8×6=48)
A : B : C = 6 : 10 : 21. (Scale A:B ×2 → 6:10; Scale A:C ×3 → 6:21)
Map distance = 7.5 cm → 7.5 × 40 000 = 300 000 cm = 3 km. Actual = 3.2 km. Error = (3.2−3)/3.2 × 100 ≈ 6.25%
Max brass: 180 g Cu → needs 120 g Zn. 120 ≤ 100, so zinc is limiting. 100 g Zn → needs 150 g Cu (ratio 3:2). Max brass = 250 g. Left: 30 g copper, 0 g zinc.
8 people: eggs = 1 part. Let x = egg mass. Total = 4x for 8 people. For 20 people: scale ×2.5. If 1 egg = 60 g, ratio means 60 g eggs : 180 g flour per batch. For 20 people: 2.5 × 60 = 150 g eggs (≈ 3 eggs ≈ 75p); 2.5 × 180 = 450 g flour = £1.08. Total ≈ £1.83
Actual dimensions: 6×200=1200 cm=12 m and 4.5×200=900 cm=9 m. Area = 12 × 9 = 108 m²