# Proportional or directly proportional

## Directly proportional

We know proportional means comparing two ratios by putting an equals sign in.

And directly means divide them.

Directly proportional is on top of each other or divide.

Example 1

if 8 apples cost £4.00

a total of 24 apples cost £12.00

This is shown by

8:4=24:12

or 8/4=24/12

Example 2

The length of a 1kg rope is 5m. If the weight of the rope and its length are in proportion what would be the weight of a 15m rope?

 1kg:5m = xkg:15m 1/5 = x/15

Multiply both sides by 15 to get x on its own.

 (1times15)/5 = (xcancel15)/cancel15 x = (1times15)/5 x = 15/5 x = 3

The weight of a 15m rope is 3kg.

Example 3

20 pencils cost £3.16. How much would

30 pencils cost?

20 pencils : £3.16=30 pencils :x

20/(3.16)=30/x

Rearanging the formula

x=(30times3.16)/20

x=(3times3.16)/2

x=4.74

30 pencils cost £4.74.