Succeed with maths – Part 1

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# 2 Ratios

The media reports that ‘one in three people rejects technology such as computers and mobile phones’. Alternatively, you could say that ‘for every one person who rejects technology, there are two people who embrace it’. Mathematically, we say that ‘the ratio of people who reject technology to those who embrace technology is one to two’. You can visualise this by dividing the group into those that rejected technology and those who accepted it, in the first group there would be one person and the other group two – hence the ratio one to two.

This ratio of those who reject technology to those that accept technology could be written as or in colon notation as 1:2. The colon simply replaces the line separating the top and bottom of the fraction. Ratios provide us with yet another way to convey information.

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). We have 14 wins over 8 losses, or . If you were a sports reporter you may well leave this as an improper fraction, 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.