WORKPLACE MATHS · TEXTBOOK LESSON
A percentage is a fraction out of 100. Percentages make it easy to compare proportions, calculate increases and decreases, and interpret rates in everyday and scientific contexts.
Learning objectives
By the end of this lesson, you should be able to:
- Convert between fractions, decimals and percentages.
- Find a percentage of a quantity.
- Calculate percentage increase and decrease.
- Use reverse percentages where the original value is unknown.
1. Key vocabulary and definition
Definition
p% means p/100. For example, 35% = 35/100 = 0.35.
percentpercentage multiplierincreasedecreaseoriginal value
2. Essential facts and rules
These are the facts you should know before attempting the worked example.
Key mathematical facts
- To find p% of an amount, multiply by p/100.
- A 12% increase uses the multiplier 1.12.
- A 12% decrease uses the multiplier 0.88.
3. Standard method
A reliable method helps prevent errors and makes your reasoning easy to follow.
1
Convert the percentage to a decimal multiplier.
2
Multiply by the original amount.
3
For percentage change, compare change with the original: change/original × 100%.
4
For reverse percentage, divide the final value by the multiplier.
5
Check whether the result should be larger or smaller than the starting value.
4. Worked example
Worked example
A jacket costs 240 AED and is reduced by 15%. Find the sale price.
1
15% = 0.15, so the decrease is 240 × 0.15 = 36.
2
Subtract the decrease: 240 - 36 = 204.
3
Alternatively use the multiplier 0.85: 240 × 0.85 = 204.
4
Sale price = 204 AED.
5. Common mistakes
Watch out for these
- Starting calculations before deciding what the question is asking.
- Skipping important steps or changing notation midway through a solution.
- Accepting an answer without checking whether its size, sign or unit is sensible.
6. Video lesson
This topic is ready for a matching video lesson. The written textbook lesson is fully available now; additional videos can be added to the same lesson template.
7. Practice exercise
Complete these without looking at the answers first.
- Write 62% as a decimal.
- Find 25% of 360.
- Increase 80 by 15%.
- A price falls from 250 to 225. Find the percentage decrease.
- After a 20% discount, an item costs 96. Find the original price.
Show answers
- 0.62
- 90
- 92
- 10%
- 120
8. Chapter summary
- Understand the underlying idea before memorising a procedure.
- Use precise mathematical notation and show a logical method.
- Always check the final result.