GCSE Maths Practice: direct-proportion

Direct Proportion in Recipe Scaling

Direct proportion is a key idea in GCSE Maths and is often tested using real-life contexts such as cooking and recipes. When a recipe serves a certain number of people, the quantities of ingredients are directly related to the number of servings. This means that if the number of people increases, the amount of each ingredient must increase at the same rate.

In direct proportion problems, each person is assumed to need the same amount of food. This allows the recipe to be scaled up or down accurately. Understanding this relationship helps students solve exam questions confidently and also apply maths skills in everyday life.

Finding the Amount per Person

The most reliable way to solve recipe-based proportion problems is to find the amount needed for one person first. This is sometimes called the unit amount. Once this value is known, it can be multiplied by any number of people.

Example: A recipe uses 300 g of rice to serve 6 people. To find the amount per person, divide 300 g by 6, which gives 50 g per person. If the recipe needs to serve 9 people, multiply 50 g by 9 to find the new total amount of rice.

Scaling Recipes Using Multiples

Another approach is to scale the quantities directly when the number of people increases by a simple factor.

Example: If a recipe for 3 people uses 150 g of vegetables, then a recipe for 6 people will use twice as much, which is 300 g. Both the number of people and the ingredient amount double, 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.
• Assuming ingredient amounts do not scale evenly.

A quick sense check is helpful. Serving more people should always require more ingredients.

Real-Life Applications

This type of calculation is used regularly outside the classroom. Home cooks adjust recipes for family meals, restaurants prepare food for different group sizes, and catering companies calculate ingredient quantities for large events. For example, if one portion of soup requires 250 ml of water, then 12 portions will require twelve times that amount.

Frequently Asked Questions

Do all ingredients follow direct proportion?
Most main ingredients do, but small items like spices may not scale exactly in real life.

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

Study Tip

For GCSE Maths questions involving recipes, always start by writing down how much is needed for one person. This creates a clear structure and helps you stay organised under exam conditions.