2.2 Ratios in recipes

So far, you have worked with ratios as fractions. Remember that ratios are also given in colon notation. For example, a recipe may call for two cups of raisins for every three cups of oatmeal. This can be written as the ratio 2:3. If you decided to make more or less of recipe, you need to preserve the ratio. In other words, there would need to be two parts raisins for every three parts oatmeal. Let’s look at an example.

A recipe for shortbread requires 300 g of plain flour, 100 g of sugar and 200 g of butter.

This means that the ratio of flour to sugar to butter is 300:100:200. Ratios can be cancelled down like fractions. Dividing all parts of the ratio by 100, it can be expressed more simply as 3:1:2, or three parts flour, one part sugar and two parts butter.

Figure 6 Ratios in recipes

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This is a picture of the ingredients for the shortbread. Three heaps of flour, one heap of sugar and two heaps of butter are shown.

Figure 6 Ratios in recipes

Suppose you wish to make some shortbread following this recipe using 300 g of butter. How much flour and sugar will you need?

Starting with the butter, 300 g is equivalent to two parts.

So one part is the same as 300 g ÷ 2 = 150 g.

Hence, three parts will be the same as 150 g × 3 = 450 g.

So, 450 g of flour and 150 g of sugar will be needed.

Feeling a little shaky with ratios written in colon notation? Check out this interactive website and try the quizzes.

In the next section we are going to find out about the golden ratio. This occurs in many situations both in mathematics and in nature.