10.1 Simplifying ratios
Sometimes you need to work out the ratio from the quantities you have.
If we refer back to the example we discussed earlier, we said that the ratio of women to men at the drama club is 150:100. However, you can simplify this ratio by dividing all parts by the same number. This is similar to simplifying fractions, which you have done.
With 150:100, we can divide each side of the ratio by 50 (you could also divide by 10 and then by 5), so the ratio will simplify to 3:2. Therefore, the ratio of women to men at the club is 3:2. Having it written in its simplest form makes it easier to think about and to use for other calculations. For every 2 men you have, there are 3 women.
Let’s look at another example.
Example: Recipes and ratio
Look at this recipe for a mocktail:
- 50 ml grenadine
- 100 ml orange juice
- 150 ml lemonade
The ratio of the ingredients is:
- grenadine:orange juice:lemonade
- 50 : 100 : 150
To simplify this ratio you can divide all of the numbers by 50 (or by 10 and then 5).
This gives the ratio of grenadine to orange juice to lemonade as 1:2:3.
Activity 24: Simplifying ratios
Simplify the following ratios:
- The ratio of women to men in a class is 15:20.
- The ratio of management to staff in a warehouse is 10:250.
- The ratio of home to away supporters is 24 000 to 8000.
- The ratio of votes in a local election was candidate A 1600, candidate B 800, Candidate C 1200.
- The ratio of fruit in a bag of mixed dried fruit is 150 g currants, 100 g raisins, 200 g sultanas and 50 g mixed peel.
Women to men is 3:4 (divide both sides by 5).
Management to staff is 1:25 (divide both sides by 10).
Home to away supporters is 3:1 (divide both sides by 8000 or by 1000 and then by 8).
A to B to C is 4:2:3 (divide each part of the ratio by 400 or by 100 and then by 4).
Currants to raisins to sultanas to mixed peel is 3:2:4:1 (divide by 50 or by 10 and then 5).
Ratio questions can be asked in different ways. There are three main ways of asking a ratio question. Take a look at an example of each below and see if you can identify the differences.
A recipe for bread says that flour and water must be used in the ratio 5:3. If you wish to make 500 g of bread, how much flour should you use?
You are growing tomatoes. The instructions on the tomato feed say ‘Use 1 part feed to 4 parts water’. If you use 600 ml of water, how much tomato feed should you use?
Ishmal and Ailia have shared some money in the ratio 3:7. Ailia receives £20 more than Ishmal. How much does Ishmal receive?
In questions of type 1, you are given the total amount that both ingredients must add to, in this example, 500 g. In questions of type 2 however, you are not given the total amount but instead are given the amount of one part of the ratio. In this case you know that the 4 parts of water total 600 ml.
The final type of ratio question does not give us either the total amount or the amount of one part of the ratio. Instead, it gives us just the difference between the first and second part of the ratio. Whilst neither type of ratio question is more complicated than the others, it is useful to know which type you are dealing with as the approach for solving each type of problem is slightly different.