Algebraic Proportion

Algebraic Proportion

GCSE(F), GCSE(H),

A proportion can be written as a formula. The formula will consist of two variables and a constant. The constant is the multiplier to one of the variables:

`y = kx`

The conversion for miles to kilometres is:

5 miles converts to eight kilometres

and to calculate a conversion:

1 mile = `frac(5)(8)` or `m = frac(5)(8)k`

where `m` are miles and `k` are kilometres.

Examples

1. Write a conversion for a currency conversion from Euros to British Pounds. The conversion rate is 0.8 Euros for every British Pound.

Answer: `p = 0.8e`

Check that the conversion is correct: for 10 Euros, fewer Pounds are expected. 10 x 0.8 = £8.

2. A formula is shown as `x = 0.25y`. Rewrite this direct proportion to make `y` the subject.

Answer: `4x = y`

Multiply both sides of the proportion by 4.