Learning Objectives
- find a percentage of a quantity;
- calculate percentage increase and decrease;
- use multipliers efficiently;
- solve reverse-percentage problems;
- interpret percentage changes in financial contexts.
Introduction
This lesson develops Percentages in Finance from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
🎛️ Interactive Percentage Explorer
Adjust the original amount and percentage. Use the selector to compare finding a percentage, increasing and decreasing.
Amount scale
🌍 Where Will You Use This?
Percentages appear in discounts, interest, tax, commission, inflation, profit, exam marks and salary increases.
What Does Percent Mean?
Percent means “out of 100”.
Finding a Percentage of a Quantity
Find 18% of US$250.
18% = 0.18.
0.18 × 250 = 45.
18% of US$250 is US$45.
Percentage Increase and Decrease
Increase US$320 by 12%.
Multiplier = 1.12, so new amount = 320 × 1.12 = US$358.40.
Decrease US$480 by 15%.
Multiplier = 0.85, so new amount = 480 × 0.85 = US$408.
Finding Percentage Change
Reverse Percentages
A reverse-percentage question gives the value after a change and asks for the original.
After a 20% discount, a bag costs US$64. Find the original price.
After 20% off, 80% remains.
0.80 × original = 64.
Original = 64 ÷ 0.80 = US$80.
Successive Percentage Changes
Two percentage changes act on different amounts, so they should be applied one after another.
A price rises by 10%, then falls by 10%.
Overall multiplier = 1.10 × 0.90 = 0.99.
The final price is 99% of the original, so it has fallen by 1%.
💼 Money Smart Tip
A 20% increase followed by a 20% decrease does not return to the original value because the second percentage is applied to a different amount.
🔍 How Do I Recognise the Method?
- “of” → multiply.
- “increase by” → use a multiplier above 1.
- “decrease by” → use a multiplier below 1.
- “original price” after a change → reverse percentage.
- “percentage change” → change ÷ original × 100%.
✅ Quick Check
🧠 Let’s Think Together
Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.
Worked Examples
Reason through the method
- Identify the known information and what must be found.
- Choose the definition, property or formula that connects them.
- Substitute carefully and show each step.
- Check the notation, units and whether the result is sensible.
Practice Questions
Foundation- Find 12% of US$350.
- Increase US$240 by 15%.
- Decrease US$560 by 22%.
- A price rises from US$80 to US$92. Find the percentage increase.
- After a 30% discount, a phone costs US$245. Find the original price.
- A salary increases by 8% to US$540. Find the original salary.
- A price increases by 20% and then decreases by 15%. Find the overall percentage change.
- A shop reduces a price by 10% and then by a further 20%. The final price is US$216. Find the original price and the single equivalent discount percentage.
✅ Check Your Work
Show practice answers
- US$42.
- US$276.
- US$436.80.
- 15%.
- US$350.
- US$500.
- 1.20×0.85=1.02, so the overall increase is 2%.
-
Original = 216 ÷ (0.90×0.80) = US$300.
Combined multiplier = 0.72, so equivalent discount = 28%.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Percent means out of 100.
- Use multipliers for increases and decreases.
- Percentage change uses the original amount as denominator.
- Reverse percentages undo the multiplier.
- Successive changes must be applied one at a time.