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.
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Ratio Remix 🎛️
A **ratio** compares amounts — 2 parts squash to 3 parts water, a map's 1 cm to 100 000 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.
Simplest form ✂️
Simplify a ratio just like a fraction: **divide both parts by their highest common factor**. **12 : 18** — both divide by 6 — = **2 : 3**. Keep going until no whole number divides both sides. A ratio in its simplest form uses the smallest whole numbers possible.
Simplify the ratio
An interactive activity.
Match the units first 📏
A ratio only works when both quantities are in the **same unit**. Convert *before* you form it: **50 cm : 2 m** — change 2 m into 200 cm — = 50 : 200 = **1 : 4**. If you skip the conversion and write 50 : 2, you get a completely wrong answer. Same unit, every time.
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** in total. So the first amount is **3/8** of the whole, and the second is **5/8**. ⚠️ The classic slip is reading 3 : 5 as "3/5 of the total". It is **3/8** — the denominator is the **total** number of parts, not the other part.
What fraction of the total?
In the ratio 2 : 3, what fraction of the whole is the first part?
- 2/5
- 2/3
- 3/5
- 1/2
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. One part: £40 ÷ 8 = **£5**. 3. Scale up: 3 × £5 = **£15** and 5 × £5 = **£25**. Check: £15 + £25 = £40. ✓
Order the sharing method
An interactive activity.
Share it out
An interactive activity.
Best value ⚖️
Ratio thinking cracks **best-value** questions: find the cost of **one** item (or the amount per £1) and compare. A pack of 6 eggs costs £1.50 → 150p ÷ 6 = **25p each**. A pack of 10 eggs costs £2.40 → 240p ÷ 10 = **24p each**.\n\nThe 10-pack is cheaper **per egg**, so it is better value — even though it costs more overall.
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
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 _____.