An easy way to compare ratios is to represent them as straight-line graphs. The graphs below represent the two ratios 4:5 and 2:7. We can compare them by finding points which have the same x value (10 in the example below) to obtain two comparable ratios (8:10 and 2.9:10):

If x = 100 the two comparable ratios represent percentages:

Gear ratios

Most bikes work using gears. The chain goes round two wheels with teeth so that as one turns the other also turns. The rate of rotation of one gearwheel compared with the other depends on the number of teeth in the respective rims. The ‘gear ratio’ is the ratio of the rates of rotation. For example, the gearwheels of a bicycle may have 24 and 12 teeth. So the ratio of the number of rotations of the small wheel to the large wheel is 24:12 or 2:1.

Metric paper sizes

In each rectangle the ratio of the length of the long side to the short side is root(2):1.

The system of A sizes was constructed so that A0 is one square metre in area. The ratio of successive lengths is root(2):1 and the ratio of successive areas is 2:1. Therefore as A0 is one square metre in area, A1 is a half a square metre, A2 is a quarter of a square metre, A3 is one-eighth and A4 is one-sixteenth of a square metre.