Ratio & Rate
Calculate and apply ratios and rates
What is a Ratio?
A ratio compares two or more quantities. We write it with a colon (:). For example, if there are 3 boys and 5 girls, the ratio of boys to girls is 3:5. Ratios can be simplified just like fractions.
Example
Simplifying Ratios
12:8 → divide both by 4 → 3:2
15:25 → divide both by 5 → 3:5
Sharing in a ratio: R100 shared in the ratio 2:3.
Total parts = 2 + 3 = 5
Each part = R100 ÷ 5 = R20
Share 1 = 2 × R20 = R40
Share 2 = 3 × R20 = R60
What is a Rate?
A rate compares two quantities with DIFFERENT units. Speed is a rate: 60 km per hour (60 km/h). Price per item is a rate: R15 per kilogram. Rates always include 'per' or the '/' symbol.
Example
Rate Examples
A car travels 240 km in 3 hours.
Rate = 240 ÷ 3 = 80 km/h
6 apples cost R18.
Rate per apple = R18 ÷ 6 = R3 per apple
Which is cheaper: 4 pens for R20 or 6 pens for R24?
4 pens: R20 ÷ 4 = R5 each
6 pens: R24 ÷ 6 = R4 each → this is cheaper!
Note
Remember
Ratio = same units, compares parts. Rate = different units, uses 'per'. To simplify a ratio, divide both parts by their HCF. To find a unit rate, divide to get 'per one'.
Key Vocabulary
RatioA comparison of two or more quantities using a colon
RateA comparison of two quantities with different units
ProportionAn equation stating two ratios are equal
SimplifyTo reduce a ratio to its simplest form
Unit rateA rate expressed per one unit
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