Ratio and Proportion
How to read a ratio, divide a quantity in a given ratio, and use proportion (direct and inverse) to solve the scaling questions that run through data interpretation, partnership, mixtures and time-and-work.
What you will be able to do
- Express and simplify a ratio, and convert between a ratio and a fraction.
- Divide a quantity among two or more shares in a given ratio.
- Set up and solve a proportion, including inverse proportion.
- Recognise when a real problem is really a ratio problem in disguise.
What is inside this lesson
- 1What a ratio is
- 2Ratio, fraction and share
- 3Dividing a quantity in a ratio
- 4Worked example: splitting a fund
- 5Proportion: direct and inverse
- 6Worked example: inverse proportion
- 7Worked example: direct proportion
- 8Common mistakes
- 9Quick revision
- 10Practice
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What a ratio is
A ratio compares two quantities of the same kind by division. Writing the ratio of A to B as A ratio B, or as the fraction A over B, means only that A is that many times B. The ratio 3 ratio 2 tells you A is one and a half times B; it does not tell you whether A is 3 and B is 2, or A is 30 and B is 20.
Because a ratio is a comparison, it has no units and does not change when both terms are multiplied or divided by the same non-zero number. So 12 ratio 8, 6 ratio 4 and 3 ratio 2 are the same ratio. Always reduce to lowest terms before working, exactly as you would a fraction.
In bank exams ratio is rarely the whole question. It is the tool inside partnership, mixtures and alligation, ages, and most of data interpretation, so fluency here pays off across the section.
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