A ratio compares two quantities directly against each other, with no whole in sight. That is exactly why it survives being scaled.
Writing and simplifying
12 : 18 becomes 2 : 3. But units must match first: 50 cm to 2 m is 50 : 200, which is 1 : 4.
In the ratio 2 : 3 there are 5 parts altogether, so the shares are two fifths and three fifths.
Sharing in a given ratio
Add the parts, divide to find one part, then multiply out. Adding the shares back should always return the original amount.
Proportion
Two ratios are in proportion when they are equal. If 4 pens cost 60, then 4 : 60 = 7 : x, so x is 105.
6 workers take 10 days, so 12 workers take 5, not 20. More workers means less time, which is inverse proportion.
| Type | What happens | What stays fixed |
|---|---|---|
| Direct | Double one, the other doubles | Their ratio: cost per pen |
| Inverse | Double one, the other halves | Their product: total worker-days |
50 cm to 2 m written as 50 : 2 gives 25 : 1, which is the wrong way round. Convert to the same unit first, and it is 1 : 4.
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