Hello! I am Bea. Ratio is about fair shares and keeping things in proportion. Bees are good at that!
Bea’s tip: Draw equal parts. Find one part, then build the amount you need.
Share 56 counters in the ratio 3 : 5.
3 + 5 = 8 parts. One part = 56 ÷ 8 = 7.
The shares are 21 and 35. Check: 21 + 35 = 56, and 21 : 35 simplifies to 3 : 5.
A recipe for 4 people uses 300 g of rice. How much for 6 people?
One person: 300 ÷ 4 = 75 g. Six people: 75 × 6.
450 g. Check: 6 people need more rice than 4.
Sharing in the ratio 2 : 3 does not mean dividing the total by 2 and by 3. Add first: there are 5 equal parts altogether.
Simplify 18 : 30.
3 : 5: divide both amounts by 6.
Share £72 in the ratio 5 : 3.
£45 and £27: 8 parts, £9 per part; 5 × £9 and 3 × £9.
At a fixed price, 4 notebooks cost £6. How much do 7 cost?
£10.50: one costs £6 ÷ 4 = £1.50; seven cost 7 × £1.50.
Next sheet: Fractions, decimals and percentages · Explore the full lessons
Skills: RAT-01
When you make more or less of something, every amount changes by the same multiplier. A ratio table helps. A good trick is to go via one: divide to find the amount for 1, then multiply.
A pancake recipe for 4 people uses 200 g flour, 2 eggs and 300 ml milk. How much of each for 10 people?
Answer: 500 g flour, 5 eggs, 750 ml milk
Skills: RAT-02
A ratio like 3 : 5 says how many parts each person gets. Add the parts to get the total number of equal parts. Divide the total by that number to find one part. Then multiply.
Asha and Ben share 40 sweets in the ratio 3 : 5. How many does each get?
Answer: Asha 15, Ben 25
Skills: RAT-03
Sometimes you are told one amount, not the total. Match that amount to its number of parts to find one part. A difference is the same: it matches the difference in parts.
Tom : Zoe = 5 : 2. The difference is 5 − 2 = 3 parts, and that is £18.
Tom and Zoe have money in the ratio 5 : 2. Tom has £18 more than Zoe. How much does each have?
Answer: Tom has £30 and Zoe has £12
Skills: RAT-04
To find the best buy, compare the price for the same amount. Work out the price of one item, or of 100 g. The smaller unit price is the better value.
Compare the price for the same amount. 120p ÷ 5 = 24p, and 176p ÷ 8 = 22p. The 800 g pack is the better buy.
Rice costs £1.20 for 500 g or £1.76 for 800 g. Which is the better buy?
Answer: The 800 g pack (22p per 100 g)
Skills: RAT-05. Stretch: usually taught in Year 7, but some 11+ tests include it.
Speed tells you how far something goes in one hour (or one minute). Distance = speed × time. To find speed, divide distance by time.
Cover the one you want. Distance is speed × time. Speed is distance ÷ time.
A train travels 150 km in 3 hours. What is its speed? How far does it go in 4½ hours at that speed?
Answer: 50 km/h, then 225 km
Skills: RAT-06
A scale factor tells you how many times bigger or smaller every length gets. On a map, the scale says how real distances compare with the map. Always use the same units on both sides.
Scale factor 4: every length is × 4. 3 × 4 = 12 and 2 × 4 = 8. The shape stays the same, only bigger.
A map scale is 1 cm : 6 km. Two villages are 5 cm apart on the map. How far apart are they really? A model is built at 1 : 50. The real boat is 4.5 m long. How long is the model?
Answer: 30 km, and 9 cm
Level 1 is the easiest. Level 5 is a real challenge. Try each one yourself before you read the steps.
One packet has 6 biscuits. How many biscuits are in 4 packets?
Answer: 24 biscuits
A recipe makes 12 muffins using 150 g of flour. How much flour is needed for 24 muffins?
Answer: 300 g
Share £60 between Kai and Lily in the ratio 1 : 4.
Answer: Kai £12, Lily £48
A garden has red and yellow tulips in the ratio 3 : 7. There are 40 tulips. How many more yellow than red are there?
Answer: 16 more yellow tulips
A tin has blue and yellow buttons in the ratio 5 : 8. When 6 more blue buttons are added, there are the same number of blue and yellow buttons. How many buttons were in the tin at the start?
Answer: 26 buttons
Mistake code: RATIO_ADDITIVE
The mistake: Because 6 is 2 more than 4, adding 2 to 200 g of flour to get 202 g for 6 people.
Why it is wrong: Ratios work by multiplying. If you add the same amount to everything, the proportions change and the recipe tastes different.
How to avoid it: Use a ratio table or a bar model. Find one, then multiply.
The mistake: Thinking that in the ratio 2 : 7, red is 2/7 of the marbles.
Why it is wrong: 2 : 7 compares red with blue. The whole is 2 + 7 = 9 parts, so red is 2/9.
How to avoid it: Always add the parts to find the total number of parts first.
The mistake: Saying the cheaper pack (£1.20) is the better buy without checking how much you get.
Why it is wrong: A cheaper pack can have much less in it. You need the price for the same amount.
How to avoid it: Work out the price of 1 item (or 100 g) for each deal. Compare those.
The mistake: A model is 1 : 50 and the boat is 4.5 m. Writing 4.5 ÷ 50 = 0.09 and calling it 0.09 cm.
Why it is wrong: The answer is in the same unit you started with. 0.09 is in metres, not centimetres.
How to avoid it: Change to one unit first (4.5 m = 450 cm), or label your answer carefully.
Five questions, easy to hard. Use paper and have a go before you open the answer.
5 biscuits cost 60p. How much do 8 biscuits cost?
96p
One biscuit is 60 ÷ 5 = 12p. Eight biscuits cost 8 × 12 = 96p.
Share 54 stickers between Dev and Eve in the ratio 2 : 7. How many does Eve get?
42
Parts: 2 + 7 = 9. One part: 54 ÷ 9 = 6. Eve: 7 × 6 = 42 (Dev gets 12).
A box has green and orange pencils in the ratio 4 : 3. There are 28 green pencils. How many orange pencils are there?
21
4 parts = 28, so 1 part = 7. Orange: 3 × 7 = 21.
Pack A has 6 pens for £1.50. Pack B has 10 pens for £2.30. How much is one pen in the better buy?
23p
A: 150 ÷ 6 = 25p a pen. B: 230 ÷ 10 = 23p a pen. B is cheaper per pen.
On a map, 1 cm stands for 4 km. Two towns are 7.5 cm apart on the map. Dan walks the real distance at 5 km/h. How many hours does he take?
6 hours
Real distance: 7.5 × 4 = 30 km. Time = 30 ÷ 5 = 6 hours.