GCSE Maths Practice: percentages

Question 9 of 10

This GCSE Maths question asks you to calculate the number of correct answers based on a percentage score — a core skill for exams, assessments, and real-life problem solving.

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\( \begin{array}{l}\text{A student scores 75% on 200 questions. How many}\\\text{questions did they answer correctly?}\end{array} \)

Choose one option:

Always change the percentage into a decimal first (÷100), then multiply by the total. This quick method works for marks, money, and any part-of-whole calculation.

Understanding Percentages of a Total

Finding a percentage of a total is one of the most common and useful skills in GCSE Maths. It helps you determine part of a whole — for example, how many test questions were correct, what proportion of money was saved, or how much time was completed in a task. The principle is simple: convert the percentage into a decimal and multiply it by the total amount.

The general formula is:
Part = Total × (Percentage ÷ 100).

Step-by-Step Method

  1. Write the given percentage clearly. For instance, 40% means 40 parts out of 100.
  2. Convert this percentage into a decimal by dividing by 100. 40 ÷ 100 = 0.40.
  3. Multiply the total amount by 0.40 to find the required portion.
  4. The result tells you the exact part that represents that percentage.

Worked Examples (Different Values)

  • Example 1: 60% of 250 marks.
    Multiplier = 0.60 → 250 × 0.60 = 150 marks.
  • Example 2: 35% of 400 students.
    Multiplier = 0.35 → 400 × 0.35 = 140 students.
  • Example 3: 80% of £90.
    Multiplier = 0.80 → 90 × 0.80 = £72.

Common Mistakes

  • Forgetting to divide by 100: Writing 75 as 75.0 instead of 0.75 produces answers that are far too large.
  • Reversing the operation: Some students divide instead of multiply, giving a smaller incorrect value.
  • Mixing up increase/decrease problems: This type of question only finds part of a total, not a change in value.

Real-Life Applications

Percentages of totals are everywhere in everyday life. Teachers calculate the percentage of correct answers to determine grades. Employers measure employee targets in percentages. Financial planners use percentages to show how much of a budget is spent on each category. Even athletes analyse what percentage of goals or attempts are successful.

For example, a sports analyst might say that a football player scored in 60% of matches. This means the player scored in 0.60 × total matches. The same method applies when calculating what portion of a task or resource is completed or used.

Frequently Asked Questions

Q1: How can I find what percentage one number is of another?
A: Divide the part by the total and multiply by 100.

Q2: Can percentages be greater than 100?

A: Yes, if the part exceeds the total — for example, earning 120% of a goal means exceeding it by 20%.

Q3: What is the fastest way to find half or a quarter in percentage form?

A: Half is 50% (×0.5), a quarter is 25% (×0.25). Recognising these instantly saves time in exams.

GCSE Study Tip

When revising, remember that multiplying by a decimal is faster than writing separate percentage steps. Always check that your final value makes sense — it should be smaller than the total if the percentage is below 100%, and larger if it is above 100%.

Summary

Finding a percentage of a total is essential for solving everyday and GCSE Maths problems. The formula Part = Total × (Percentage ÷ 100) is straightforward and reliable. Practise it with different contexts — marks, money, or measurements — to build speed and confidence for exam success.