⚖️ Ratios & Proportions

Scaling, mixing, and fair comparisons

📊 Ratios

A ratio 3:2 means for every 3 of one thing, there are 2 of the other. Total parts = 5.

If 50 items split 3:2, that's 30 and 20
First part: (3/5) × 50 = 30
Second part: (2/5) × 50 = 20

Always add up the ratio parts to find the denominator for your fractions.

↕️ Scaling up and down

If 3 workers paint a fence in 12 hours:

1 worker takes 3 × 12 = 36 hours (less workers = more time)
6 workers take 12 ÷ 2 = 6 hours (more workers = less time)

When you double the workers, you halve the time — that's inverse proportion.

Two types: more of one means more of the other (direct), or more of one means less of the other (inverse).

🥣 Mixing

If you mix 2 parts red with 3 parts white, the mixture is 2/(2+3) = 2/5 red.

To make 10 litres: you need 4 litres red and 6 litres white
To make 35 litres: you need 14 litres red and 21 litres white

The ratio stays the same no matter how much you make!

🧠 Practice Quiz

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