Percentage Change Quizzes

Introduction

Percentage change is a fundamental concept in GCSE Maths that measures how much a quantity increases or decreases in relation to its original value. It is widely used in finance, business, science, and everyday situations such as calculating discounts, price increases, profit margins, and population changes. Understanding percentage change allows students to solve real-life problems accurately and interpret data effectively.

Core Concepts

Definition

Percentage change shows how much a quantity has increased or decreased as a percentage of its original value. It can be positive (increase) or negative (decrease).

The Formula

The general formula for percentage change is:

$$ \text{Percentage Change} = \frac{\text{Change}}{\text{Original Value}} \times 100 $$>

Where:

• Change = New Value – Original Value (for increase)
• Change = Original Value – New Value (for decrease)

Types of Percentage Change

• Percentage Increase: When the new value is greater than the original value.
• Percentage Decrease: When the new value is smaller than the original value.

Rules & Steps

1. Identify the original value and the new value.
2. Calculate the change:
   • Increase: New – Original
   • Decrease: Original – New
3. Divide the change by the original value.
4. Multiply by 100 to convert to a percentage.
5. Round to the required number of decimal places if necessary.
6. Label your answer with the % sign.

Worked Examples

1. Example 1 (Increase): A jacket originally costs £80 and is now £100. Find the percentage increase.
   Change: 100 – 80 = 20 $$ \text{Percentage Increase} = \frac{20}{80} \times 100 = 25\% $$
2. Example 2 (Decrease): A laptop costs £600 but is reduced to £450. Find the percentage decrease.
   Change: 600 – 450 = 150 $$ \text{Percentage Decrease} = \frac{150}{600} \times 100 = 25\% $$
3. Example 3 (Higher Level): A population increases from 12,000 to 13,500. Find the percentage increase.
   Change: 13,500 – 12,000 = 1,500 $$ \text{Percentage Increase} = \frac{1500}{12000} \times 100 = 12.5\% $$
4. Example 4: A car’s value decreases from £15,000 to £12,000. Find the percentage decrease.
   Change: 15,000 – 12,000 = 3,000 $$ \text{Percentage Decrease} = \frac{3000}{15000} \times 100 = 20\% $$
5. Example 5 (Compound Context): An item increases in price from £50 to £60 and then to £72. Find the total percentage increase.
   Step 1: First increase: 60 – 50 = 10 → 10 ÷ 50 × 100 = 20% Step 2: Second increase: 72 – 60 = 12 → 12 ÷ 60 × 100 = 20% Step 3: Total percentage increase is not simply additive but can be interpreted step by step in exams.

Common Mistakes

• Dividing by the new value instead of the original value.
• Mixing up increase and decrease formulas.
• Forgetting to multiply by 100 to convert to a percentage.
• Rounding too early, leading to inaccurate results.
• Not labeling the final answer with %.

Applications

• Finance: Calculating interest, discounts, and profit margins.
• Business: Price increases, sales growth, and revenue changes.
• Population Studies: Growth or decline percentages in populations.
• Exams: Often combined with ratio, proportion, and compound interest problems.

Strategies & Tips

• Always identify the original value before calculating change.
• Check whether it is an increase or a decrease to use the correct approach.
• Use brackets in calculations to avoid mistakes when using a calculator.
• Practice multi-step problems involving consecutive percentage changes.
• Convert percentages to decimals only if required for compound calculations.

Summary

Percentage change measures how a quantity changes relative to its original value. Key formulas:

• Percentage Increase: $\frac{\text{New – Original}}{\text{Original}} \times 100$
• Percentage Decrease: $\frac{\text{Original – New}}{\text{Original}} \times 100$

Consistency in using the original value, correct identification of increase or decrease, and careful calculation ensures accuracy. Mastery of percentage change enables students to solve a wide range of problems in exams and real-life contexts. Reinforce your understanding by attempting the quizzes in this subcategory and exploring step-by-step percentage change scenarios!