Ratio Remix
Ratios, mixed and mastered: simplify them, match the units first, read them as fractions, and share any amount in a given ratio, then use the same thinking to spot the best-value buy.
Get the method right under pressure
Free interactive practice on the steps that lose marks under exam pressure.
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Ratio Remix
A ratio compares amounts: 2 parts squash to 3 parts water, a map's 1 cm to 25 000 cm of real ground, £40 shared between two people. It runs through mixing, scaling, and best-value questions. Get four moves solid: simplify, match units, read as a fraction, share out, and the whole ratio topic remixes into something easy.
Match the units, then simplify
A ratio only works when both quantities are in the same unit, and the conversion comes first: - 50 cm : 2 m. Change 2 m into 200 cm, giving 50 : 200. Write 50 : 2 instead and every answer after it is wrong. - Then simplify exactly like a fraction: divide both parts by their highest common factor. 50 : 200 both divide by 50, so 1 : 4. - 12 : 18 both divide by 6, giving 2 : 3. Keep going until no whole number divides both sides.
Simplify the ratio
Written in its simplest form, 15 : 25 becomes 3 : k. What is the value of k?
Convert, then simplify
Write 80 cm : 1 m in its simplest form.
- 4 : 5
- 80 : 1
- 8 : 10
- 4 : 1
Reading a ratio as a fraction
In the ratio 3 : 5 there are 3 + 5 = 8 parts altogether. Almost every mistake here is the same one: using the wrong number underneath.
Match the ratio to the first part as a fraction
- 1 : 3
- 3 : 7
- 2 : 3
- 1 : 1
- 1/4
- 3/10
- 2/5
- 1/2
Sharing in a ratio
To divide an amount in a ratio, work in parts. Share £40 in the ratio 3 : 5: 1. Add the parts: 3 + 5 = 8 parts. 2. Find one part: £40 ÷ 8 = £5. 3. Scale up: 3 × £5 = £15 and 5 × £5 = £25. Check: £15 + £25 = £40. ✓ Finding one part is the move that unlocks everything, including the harder questions where the total is what you are asked to find.
Share it out
Share £72 in the ratio 5 : 3. How much (in £) is the LARGER share?
Work backwards
An amount of money is shared between two people in the ratio 3 : 5. The SMALLER share is £15. What is the TOTAL amount, in £? (Find one part first.)
Two jobs ratio does for you
Both of these are the same trick: get everything down to one of something, then compare or scale up.
Read the map
A map has a scale of 1 : 25 000. Two towns are 6 cm apart on the map. How far apart are they in real life?
- 1.5 km
- 150 km
- 15 km
- 0.24 cm
Which is better value?
Which is better value: 4 pens for £2.00, or 10 pens for £4.50?
- 10 pens for £4.50 (45p each)
- 4 pens for £2.00 (50p each)
- They are the same value
- You cannot compare different pack sizes
Mix the concrete
Concrete is mixed from cement, sand and gravel in the ratio 1 : 2 : 4. A builder has 15 kg of cement, and plenty of sand and gravel.
- How many parts are there altogether in the mix?
- The cement is 1 part, and he has 15 kg of it. How much sand does he need?
- How much concrete can he make in total?
Ratio survival rules
To simplify a ratio, divide both parts by their highest common _____. Before forming a ratio, put both quantities in the same _____. To share an amount in a ratio, add the parts, then divide the amount by the total number of parts to find the value of one _____. And on a map with a scale of 1 : 25 000, every 1 cm on the paper stands for 25 000 cm on the _____.