GCSE Maths Practice: percentages

Question 6 of 10

This GCSE Maths question focuses on calculating new values after a percentage increase — a key skill used in finance, population growth, and general problem solving.

‹ ›

\( \begin{array}{l}\text{A product costs 450. If the price increases by 12%,}\\\text{what is the new price?}\end{array} \)

Choose one option:

When increasing by a percentage, always use the multiplier form (1 + rate). It saves time and prevents confusion between increase and decrease problems.

Understanding Percentage Increases

Percentage increases are used to describe how much a number grows compared with its original value. In GCSE Maths, this concept appears in topics such as financial growth, interest rates, and population change. When something increases by a certain percentage, it means we add that proportion of the original value to itself.

The general rule is: New Value = Original × (1 + Percentage Increase).

Step-by-Step Method

  1. Change the percentage increase into a decimal by dividing by 100. For example, 8% = 0.08.
  2. Add 1 to this decimal: 1 + 0.08 = 1.08.
  3. Multiply the original number by 1.08 to get the new total.
  4. The answer represents the new amount after the increase.

Worked Examples (Different Values)

  • Example 1: A bicycle costs £250 and the price rises by 10%.
    Multiplier = 1.10 → 250 × 1.10 = £275.
  • Example 2: A cinema ticket costs £12 and the price rises by 5%.
    Multiplier = 1.05 → 12 × 1.05 = £12.60.
  • Example 3: A school population of 800 grows by 6%.
    Multiplier = 1.06 → 800 × 1.06 = 848 students.

Common Mistakes

  • Forgetting to add 1: Using 0.08 instead of 1.08 only gives the size of the increase, not the total value.
  • Using the wrong sign: Adding the percentage for a decrease or subtracting it for an increase leads to errors.
  • Incorrect decimal form: Writing 8 instead of 0.08 multiplies the answer by ten!

Real-Life Applications

This calculation is used in many areas of daily life. Employers use it for annual pay rises, banks apply it to calculate interest on savings, and economists use it to track inflation. Businesses also measure sales growth as a percentage increase from the previous year. Understanding this concept helps students make sense of real-world data and financial decisions.

Frequently Asked Questions

Q1: What is the difference between a 10% increase and adding 10?
A: A 10% increase depends on the original value, while adding 10 is a fixed amount. For example, 10% of 200 is 20, not 10.

Q2: Can there be more than one increase in a question?

A: Yes. Apply each increase step by step. For example, two 5% rises: 100 × 1.05 × 1.05 = 110.25.

Q3: How can I check my answer quickly?

A: If the value increases, the new amount should be greater than the original. The difference should roughly match the percentage size.

GCSE Study Tip

Always convert the percentage into a decimal and use the multiplier form. The multiplier for an increase of x% is 1 + (x ÷ 100). Writing the full expression helps prevent sign errors and keeps calculations clear.

Summary

Percentage increases are essential in GCSE Maths and everyday reasoning. Remember: multiply by (1 + percentage/100) to find the new value. Practise using different numbers and contexts, such as prices, wages, and populations, to master this important topic.