Proportion - Recipes

A recipe lists how much of each ingredient you need to make a certain number of items or portions. To make a different number of the same size, every ingredient must change in the same way.

If you make three times as many biscuits, you need three times as much of every ingredient. If you make half as many, you need half as much of each one. This is called direct proportion.

In the exam you are usually given a list of ingredients and asked how much of one ingredient, or of each one, is needed for a different number, for 2 or 3 marks. Harder questions, for 3 or 4 marks, ask whether someone has enough of every ingredient, how much more they need, or the greatest number they can make.

Often the number you want is not two or three times the number in the recipe, such as 12 cupcakes to 18 cupcakes. Build it up from parts of the recipe that are easy to find.

• Half the recipe: divide each amount by 2
• Two recipes: multiply each amount by 2
• Add the parts you need: 18 cupcakes is 12+6, one recipe plus half a recipe.

Or find the scale factor, the number you multiply every amount by. Divide the number you want by the number in the recipe: 18\div12=1.5

Write what each number stands for, such as "6 cupcakes: 45 g butter". Labels stop you losing track in a longer question.

Another way is to find the amount for one item first, then multiply. It always works, and it is the best choice when the numbers do not build up neatly, such as 8 items to 5 items.

• Divide the amount in the recipe by the number the recipe makes. This is the amount for one.
• Multiply the amount for one by the number you want.

The same method works for prices when every item costs the same. If 4 tickets cost £34, one ticket costs 34\div4=\pounds 8.50, so 7 tickets cost \pounds 8.50\times7=\pounds 59.50

Ingredients are often sold in packs or bags. You cannot buy part of a pack, so when a division gives a decimal, round up. If you need 3.2 packs, you must buy 4 packs.

When you work out how many items you can make, round down instead. If the flour is enough for 26.7 cakes, you can make only 26 whole cakes.

Work out how much of each ingredient is needed, then compare it with what the person has. Compare grams with grams and millilitres with millilitres: 1 kg =1000 g and 1 litre =1000 ml.

Check every ingredient. Having plenty of one ingredient does not make up for being short of another.

Finish with a clear decision, such as "No, she needs 40 ml more milk." Correct numbers with no decision do not answer the question.

Here you know how much of each ingredient there is. For each ingredient, find how many items it is enough for: divide the amount you have by the amount one item needs.

Every item needs all of the ingredients, so the answer is the smallest of these numbers. That ingredient runs out first.

Part of a batch still counts. If the butter is enough for 4.5 batches of 10 muffins, you can make 45 muffins, not just 40

• Multiplying by the number wanted. The amounts are for the whole recipe, not for one item, so find the scale factor first.
• Adding instead of multiplying. Going from 20 to 30 biscuits does not mean adding 10 g to each amount; add half the recipe instead.
• Counting batches wrongly. Doubling twice makes four lots, not three: 20, then 40, then 80 is four lots of 20.
• Stopping at whole batches. Half a batch can still be made, so 4.5 batches of 10 is 45 items.
• Checking only some ingredients. Work out every ingredient, because any one of them can run out first.
• Leaving out the decision. End by saying whether there is enough, and what is short.