What a ratio tells you
A ratio compares two or more quantities of the same kind, for example 2 : 3. Because a ratio behaves like a fraction, it is simplified in the same way, by dividing every part by their highest common factor. Thus 12 : 18 = 2 : 3. A ratio can also be written in the form 1 : n, which is especially useful for map scales.
Key idea
To share an amount in a ratio, add the parts to find the total number of shares, divide the amount by that total, then multiply by each part.
Sharing in a given ratio
Worked example
Share RM60 between two people in the ratio 2 : 3.
Total shares = 2 + 3 = 5.
One share = RM60 ÷ 5 = RM12.
Amounts = 2 × RM12 = RM24 and 3 × RM12 = RM36.
Check: RM24 + RM36 = RM60. ✓
Direct and inverse proportion
In direct proportion two quantities increase in the same ratio, so y = kx and their graph is a straight line through the origin. In inverse proportion one quantity increases as the other decreases, so y = k/x and their product stays constant. For example, if 8 workers take 6 days, the work is 8 × 6 = 48 worker-days, so 12 workers take 48 ÷ 12 = 4 days.
Remember
- A ratio has no units.
- Keep the order of the quantities the same.
- Map scale 1 : 50000 means 1 cm represents 50000 cm = 0.5 km.