Writing a Ratio as a Fraction or Linear Function
Writing a ratio as a fraction or linear function means converting a ratio such as a:b into the fraction b/a (or a/b), then into an equation such as y = kx that shows how the two quantities are related. It builds on simplifying ratios and appears in GCSE algebra and proportion questions that ask you to express one quantity directly in terms of another.
Before you start
Make sure you're comfortable with these topics first:
Method
- Write the given ratio in its simplest form by dividing both parts by their highest common factor.
- Decide which quantity you need as a fraction of which, then write that ratio as a fraction (numerator = the quantity you are describing, denominator = the quantity you are comparing it to).
- To write one quantity as a linear function of the other, set up the equation (quantity)/(other quantity) = the fraction from the ratio, then rearrange to the form y = kx.
- Check the constant k is fully simplified, as a fraction or a decimal.
- Substitute any given value into the function to find an unknown quantity, showing your working.
- Check your answer makes sense: if the ratio shows one quantity is bigger than the other, then k should be greater than 1, and vice versa.
Worked example
The ratio of Jamal's stickers to Aisha's stickers is J:A = 3:7. Write A as a linear function of J, and use it to find the number of Aisha's stickers when Jamal has 24 stickers.
- Write A as a fraction of J using the ratio: A/J = 7/3.
- Rearrange to make A the subject: A = 7/3 x J.
- Substitute J = 24 into the function: A = 7/3 x 24.
- Work out the calculation: A = (7 x 24)/3 = 168/3 = 56.
- State the final answer: Aisha has 56 stickers.
Practice questions
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Exam-style questions
Written in the style of a GCSE Maths exam paper, with a full mark scheme.
Simplify the ratio 18:30 fully, and hence write the first quantity as a fraction of the second quantity.
x and y are two quantities such that x:y = 5:6. (a) Write y as a fraction of x. (1) (b) Hence write y as a linear function of x, in the form y = ... x. (2)
Two investments, P and Q, are in the ratio P:Q = 5:8. Investment P is worth 350 pounds. (a) Write Q as a linear function of P. (2) (b) Calculate the value of investment Q. (2)
Free printable worksheet
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