GCSE Maths Practice: direct-proportion

Direct Proportion and Unit Pricing

Direct proportion is a common GCSE Maths topic that helps you compare quantities that change at the same rate. When two values are directly proportional, increasing one value causes the other to increase in the same proportion. This idea is frequently used in everyday situations involving money, quantities, distance, and time.

In shopping problems, direct proportion usually means that the cost depends on how many items you buy. If each item costs the same amount, then the total cost increases steadily as more items are added. Understanding this relationship allows you to calculate prices accurately and efficiently.

The Unit Cost Method

The most reliable way to solve direct proportion cost questions is by finding the unit cost first. The unit cost is the price of a single item. Once this is known, it can be multiplied by any quantity to find the total cost.

Example: If 4 pens cost £6.00, the cost of one pen is found by dividing £6.00 by 4, giving £1.50 per pen. If someone buys 7 pens, the total cost can be calculated by multiplying £1.50 by 7, which gives £10.50.

Scaling Quantities

Some direct proportion problems can also be solved by scaling up from the original quantity. This works best when the new quantity is a simple multiple of the original amount.

Example: If 2 bottles of juice cost £3.20, then 6 bottles (three times as many) will cost three times £3.20, which is £9.60. Because both quantities increase by the same factor, the relationship remains proportional.

Common Errors to Watch For

• Dividing by the wrong number when finding the unit cost.
• Multiplying before finding the cost of one item.
• Assuming prices change when quantities change.
• Forgetting to check whether the final answer is reasonable.

A quick sense check helps avoid mistakes. If you buy more items, the cost should be higher than before.

Real-Life Uses of Direct Proportion

Direct proportion appears in many real-life situations. Supermarkets use unit pricing to compare deals, employers calculate wages based on hours worked, and recipes are adjusted based on the number of people being served. For example, if one portion of soup requires 250 ml of water, then four portions will require four times that amount.

Frequently Asked Questions

Do all money problems use direct proportion?
No. Some problems involve discounts or special offers, which may not be directly proportional.

Why is the unit cost method recommended?
It reduces confusion and works for any quantity, making it ideal for exam questions.

Study Tip

When revising GCSE Maths, practise writing each step clearly. Even if a small calculation error occurs, showing the correct method can still earn valuable method marks.