How to Scale Recipe Proportions with the Table of Joy
An example of proportions that often comes up in maths exams concerns the amount of each ingredient you need for a recipe. You can use the Table of Joy to figure out how to scale a recipe. The recipe is proportional to the number of people the dish feeds. If you double all of the ingredients, you can feed twice as many people with the end result.
The reason the Table of Joy works in so many topics is that quite a lot of maths – particularly in the numeracy curriculum and at GCSE – is based on proportional quantities, and that’s exactly what the Table of Joy handles best.
One kind of proportion question seems to come up more often than any other in maths exams, and it involves scaling recipes. Imagine you have a recipe that serves a certain number of people, but you need to cook for a bigger or smaller party. The amount of each ingredient you need is proportional to the number of people it serves, so you need to adjust the quantities to account for your head count.
A typical maths exam question looks something like this:
Here are the ingredients for a recipe for a cake that serves four people:
100g self-raising flour
150g caster sugar
You want to make a cake that serves ten people. How much caster sugar do you need?
You can solve this question using the Table of Joy:
If you’re comfortable with decimals, you can work out that one portion would be 37.5 grams, so ten portions would require 375 grams.
Here’s another example, now you’re in the swing of things:
A 10 kilogram bag of cement has this recipe on the side of it: ‘To make 100 kilograms of concrete, mix 10 kilograms of cement with 75 kilograms of aggregate, and 15 litres of water.’
Unfortunately, you don’t need 100 kilograms of concrete. You need 20 kilograms for the swimming pool you want to build in your dream mansion.
To scale the recipe down, look at the aggregate (the other ingredients work just the same way).
You need (75 x 20 ÷ 100) kilograms of aggregate, which works out to 15 kilograms. In the same way, you find that you need 2 kilograms of cement and 3 litres of water.
Another way of doing this sum is to work out the scale factor – how many times more concrete are you making? In this case, you're making a fifth as much concrete as the recipe is for, so you need to find a fifth of each ingredient.
A fifth of 75 is 15 – so you need 15 kilograms of cement, just like before. You can check the other amounts too, if you like.
This method has two possible problems: the scale factor may not be obvious, and you may end up with an especially ugly fraction sum.