4 Ratios
We often think that there will be roughly the same number of men and women in a population. But is that really true? A report in 2019 (Human Rights Watch, 2019) said we should be ‘worrying about the women shortage’. The World Health Organisation says that 105 boys are born for every 100 girls, and in some countries the ratios are more extreme, for example up to 120 boys born for every 100 girls. You can visualise this by dividing the group into men and women. If the ratio is 105 to 100, then if there were 105 in the males group, there’d be 100 in the females group. Mathematically, you would write this as a ratio 105:100 (or for the more extreme one, 120:100). The colon in between tells you it’s a ratio.
This ratio of men to women could be written as or in colon notation as 105:100. The colon simply replaces the line separating the top and bottom of the fraction. Ratios provide us with yet another way to convey information.
Note, it’s important to say which way round the ratio is! In this instance 105:100 means 105 men to 100 women, so we needed to know it was men: women not women: men.
Now consider the following example.
After 22 rounds of the Rugby Union Premiership in the 2012/2013 season, Northampton Saints had won 14 matches and lost eight. What is the ratio of wins to losses for the team?
The ratio of wins to losses can be set up as a fraction, placing the wins in the numerator (the top of fraction) and the losses in the denominator (the bottom of fraction). Northampton Saints have 14 wins over 8 losses, or . If you were a sports reporter you may well leave this as it is, but in maths you would want to show these in the simplest form, to reduce any numbers to those that are easiest to handle. You’ll probably agree that the smaller a whole number is, the easier it is to carry out calculations with! So you would simplify this as follows by dividing the numerator and denominator by 2:
Thus, the ratio of wins to losses is or 7:4 (7 to 4).
One place that you may encounter ratios is in scale models of the real world – one very common model of the real world is a map. Maps use ratios to tell you how the distances on the map relate to the actual distances in the real world and are usually called scales. If you have a scale of 1:25 000 (said as 1 to 25 000), this means that for every 1 unit measured on the map, the unit in real life is 25 000. So to convert from map distances to real distances, you need to multiply by 25 000.
For now though you'll look at an example of ratios using recipes.