GCSE Maths Practice: direct-proportion

Question 1 of 10

This question tests your ability to use direct proportion to calculate costs.

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\( \begin{array}{l}\text{2 kg of rice costs £3.40.} \\ \text{What is the cost of 5 kg of rice?}\end{array} \)

Choose one option:

Finding the cost per unit makes direct proportion questions much easier.

Understanding Direct Proportion in Real-Life Contexts

Direct proportion is a key topic in GCSE Maths and appears frequently in everyday situations such as shopping, travel, and cooking. Two quantities are said to be in direct proportion when they increase or decrease at the same rate. In simple terms, if one quantity doubles, the other quantity also doubles. This makes direct proportion especially useful when dealing with prices, weights, distances, and time.

In cost-based problems, direct proportion usually means that the price depends directly on how much you buy. If the cost of an item per unit stays the same, then buying more units will increase the total cost in a predictable way. Understanding this idea allows you to scale prices up or down confidently.

The Unit Rate Method

One of the most reliable methods for solving direct proportion problems is the unit rate method. This involves finding the value for one unit first, then using that value to calculate the cost for any other number of units. This method is particularly helpful at Foundation level because it is clear, structured, and easy to check.

Example: Suppose 3 kg of apples cost £4.20. To find the cost of 1 kg, divide £4.20 by 3, giving £1.40 per kg. If you wanted to buy 6 kg, you would multiply £1.40 by 6, resulting in £8.40.

Scaling Without Using Unit Cost

Sometimes, you can also solve direct proportion problems by scaling quantities up or down directly. This works well when the target amount is a simple multiple of the given amount.

Example: If 4 notebooks cost £6, then 8 notebooks (double the amount) would cost £12. Since both quantities double, the total cost doubles as well.

Common Mistakes to Avoid

  • Multiplying instead of dividing when finding the cost per unit.
  • Forgetting that prices must scale at the same rate as quantities.
  • Mixing up kilograms, grams, or other units without converting properly.

Always pause to check whether your final answer is sensible. If the quantity increases, the total cost should also increase.

Real-Life Applications

Direct proportion is used constantly in real life. Supermarket pricing, fuel costs, pay per hour, and recipe adjustments all rely on this principle. For example, if a recipe for 2 people uses 150 g of pasta, then cooking for 6 people would require three times that amount.

Frequently Asked Questions

Do I always need to find the unit cost?
Not always, but it is usually the safest and clearest approach, especially in exams.

How do I know it is direct proportion?
If the cost per unit stays the same and quantities increase together, the situation involves direct proportion.

Study Tip

When revising GCSE Maths, practice writing out each step clearly. This reduces errors and helps you gain method marks even if you make a small arithmetic mistake.

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