Fully worked, step-by-step solutions to GCSE Ratios, fractions and linear functions questions. See exactly how to solve problems on ratio to fraction, multiplier, ratio to gradient, line through origin.
Read the ratio
For every 4 parts of x there are 3 parts of y, so every point on the line has the form (x, y) = (4t, 3t).
Divide y by x to get the multiplier
The multiplier is y divided by x — the y-part of the ratio over the x-part, not the other way round.
State the answer
y is three quarters of x. Note the 3 (the y-part) is on top.
Read the ratio
For every 5 parts of x there are 2 parts of y, so every point on the line has the form (x, y) = (5t, 2t).
Draw the line through the origin
Starting at the origin, a run of 5 and a rise of 2 reaches the line, so the gradient is 2/5.
State the answer
The gradient equals the multiplier: y-part over x-part.
Write the sentence as an equation
"y is 2/3 of x" means multiply x by 2/3 to get y.
Turn the multiplier into a ratio
Take ; then . So the pair fixes the ratio .
State the answer
The x-part is the denominator, the y-part the numerator.
Use the point given
The line passes through the origin and through (4, 6), so those two coordinates are in the ratio 4 : 6.
Divide y by x to get the multiplier
The multiplier is y divided by x — the y-part of the ratio over the x-part, not the other way round.
State the answer
Gradient = rise / run = .
Use the point given
The line passes through the origin and through (10, 4), so those two coordinates are in the ratio 10 : 4.
Cancel the ratio
Divide both parts by the highest common factor, 2.
State the answer
Every point on the line has x and y in the ratio 5 : 2.
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