Recipe problems

Topic guide

What this worksheet practises

This worksheet focuses on scaling recipes up or down to feed a different number of people. This is a classic application of direct proportion: if you double the people, you must exactly double every single ingredient.

Key method

The most foolproof method is the "Unitary Method" – finding out exactly how much of an ingredient is needed for just one person first.

• Look at the recipe. It will tell you how many people it serves (e.g., Serves 4).
• Find the "One Person" amount: Take an ingredient and divide its quantity by the original number of people. This tells you how much is needed to feed exactly 1 person.
• Scale Up: Multiply this "One Person" amount by the new number of people you want to feed.
• Repeat this two-step process (divide, then multiply) for every ingredient requested in the question.

Worked example

A recipe for 6 people requires 300g of flour. How much flour is needed to make the recipe for 8 people?

Step 1: Find the amount for 1 person by dividing the ingredient by the original number of people.

300g ÷ 6 = 50g.

So, 1 person needs 50g of flour.

Step 2: Scale it up. We want to feed 8 people, so we multiply our 1-person amount by 8.

50g × 8 = 400g.

The final answer is 400g.

Common mistakes to avoid

The most common mistake is trying to add or subtract instead of multiplying and dividing. For example, a student sees the people go from 6 to 8 (an addition of 2), so they just add 2 onto the ingredients (300g + 2 = 302g). This is completely wrong. Recipes use multiplicative proportion, never additive.

Things to remember

If the new number of people is a very easy multiple of the old number, you can skip the unitary method. If a recipe serves 4, and you need it for 12, you can just multiply everything directly by 3 (because 4 × 3 = 12). However, the unitary method works every single time, even for awkward numbers like scaling from 7 people to 11 people.