Succeed with maths – Part 1

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# 2.1 Ratios in recipes

So far, you have worked mainly with ratios as fractions but you know 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 of oatmeal, however much of each ingredient you were using. Here is 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 2).

Figure 2 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.

Now have a go yourself at this similar, and final, activity of the week.

## Activity 7 Chocolate chip cookies

Timing: Allow approximately 10 minutes

A recipe for chocolate chip cookies requires 48 tablespoons of flour, 16 tablespoons of sugar, and 32 tablespoons of chocolate chips.

• a.What is the ratio of flour to sugar to chocolate chips?

48:16:32, which simplifies to 3:1:2 (through division by 16).

• b.If you only have 36 tablespoons of flour, how many tablespoons of sugar and chocolate chips do you need to maintain the recipe’s taste and consistency?

Three parts of flour is equivalent to 36 tablespoons. So, one part is equivalent to 12 tablespoons. Thus, you will need 12 tablespoons (36 ÷ 3). Thus, you will need 12 tablespoons of sugar and 24 tablespoons of chocolate chips.

• c.Suppose you have 40 tablespoons of chocolate chips, and plenty of everything else. Determine the amount of flour and sugar you will need if you want the maximum number of cookies you can make with your 40 tablespoons of chocolate chips.

In this case, two parts of chocolate chips will be equivalent to 40 tablespoons. So, one part is equivalent to 20 tablespoons (40 ÷ 2). Thus, you will need 3 × 20 = 60 tablespoons of flour and 1 × 20 = 20 tablespoons of sugar.