4.1 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. The video below shows an example.

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NARRATOR:

A recipe for shortbread requires 300 grams of plain flour, 100 grams of sugar, and 200 grams of butter. This means that the ratio of flour to sugar to butter is 300 to 100 to 200.

Now, ratios can be cancelled down, like fractions. Dividing all parts of this ratio by 100, it can be expressed more simply as 3 to 1 to 2, or 3 parts flour to 1 part sugar to 2 parts butter.

Now, suppose you wish to make some shortbread following this recipe using 300 grams of butter. How much flour and sugar would you need?

Well, starting with the butter, 300 grams is equal to 2 parts. So 1 part is 300 grams divided by 2. That's 150 grams. So 3 parts will be the same as 150 grams times 3. That makes 450 grams. So we need 450 grams of flour and 150 grams of sugar.

Now, say you wanted to batch-cook the shortbread using 6 kilograms of flour. How much sugar and butter will you need this time?

Using the same ratio as before, 6 kilograms is equivalent to 3 parts. So 1 part equals 2 kilograms, and 2 parts equal 4 kilograms. So to make the shortbread with 6 kilograms of flour, you would need 2 kilograms of sugar and 4 kilograms of butter.

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Now have a go yourself at something similar in the final activity of the week.