GCSE Maths Practice: direct-proportion

Direct Proportion in Recipes and Cooking

Direct proportion is commonly used when adjusting recipes to serve a different number of people. In GCSE Maths, these problems help you understand how quantities scale when everything increases or decreases at the same rate. When a recipe is adjusted correctly, all ingredient amounts change in proportion to the number of people being served.

If the number of people increases, the amount of each ingredient must also increase by the same factor. This only works when each person requires the same amount of food. Understanding this idea is important both for exam questions and for real-life situations such as cooking, baking, and catering.

Finding the Amount per Person

The safest way to solve recipe-based proportion problems is to find how much of an ingredient is needed for one person. This is called the unit amount. Once the amount per person is known, it can be multiplied by the new number of people.

Example: A recipe for 5 people uses 250 g of rice. To find the amount per person, divide 250 g by 5, which gives 50 g per person. If the recipe is adjusted to serve 8 people, multiply 50 g by 8 to find the new total amount of rice.

Scaling Recipes Up and Down

Some recipe questions can also be solved by scaling the quantities directly, especially when the new number of people is a simple multiple of the original number.

Example: If a recipe for 2 people needs 100 g of cheese, then a recipe for 4 people (double the number) will need 200 g of cheese. Both the number of people and the ingredient amount have doubled, so the relationship remains directly proportional.

Common Mistakes to Avoid

• Dividing by the wrong number when finding the amount per person.
• Forgetting to multiply by the new number of people.
• Mixing up grams and kilograms without converting.
• Assuming ingredients do not scale evenly.

Always check whether your final answer makes sense. Serving more people should require more ingredients, not less.

Everyday Uses of This Skill

This type of calculation is used regularly outside of exams. Home cooks adjust recipes based on guests, bakeries prepare batches for different order sizes, and catering companies plan ingredient quantities for large events. For example, if one sandwich needs 2 slices of bread, then 12 sandwiches will need 24 slices.

Frequently Asked Questions

Do all recipes follow direct proportion?
Most basic recipes do, but some ingredients such as spices may not scale perfectly in real life.

Why is the per-person method recommended?
It works for any number of people and reduces errors in exams.

Study Tip

In GCSE Maths questions involving recipes, always write down the amount needed for one person first. This creates a clear structure and helps you avoid mistakes under time pressure.