Number · StudentHub Lesson
Percentages
Working with percentages, percentage change and reverse percentages.
What you will learn
- Convert between fractions, decimals and percentages
- Find a percentage of an amount
- Calculate percentage increase and decrease
- Use multipliers
- Solve reverse percentage problems
Watch the lesson
We haven’t confirmed a lesson video that matches this topic closely enough yet, so the notes below are the lesson for now. A recommended video will be added once we’ve checked one properly.
Topic notes
Main Idea
A percentage is a number out of 100. Percentages let us compare amounts of different sizes and describe change.
Key Concepts
- Percent means 'per hundred'
- To find x% of an amount, multiply by x/100
- Percentage change = change ÷ original × 100
- A multiplier combines a change into one number (e.g. +20% is ×1.2)
- Reverse percentages divide by the multiplier
Definitions
- Multiplier: The decimal you multiply by to apply a percentage change.
- Percentage change: The change in a value expressed as a percentage of the original value.
- Reverse percentage: Finding the original amount before a percentage change.
Worked Example
A jacket costs ₹1,200 after a 20% discount. What was the original price?
- A 20% discount means you pay 80% of the original
- The multiplier is 0.8
- Original = 1200 ÷ 0.8
Answer: ₹1,500
Common Mistakes
- Dividing the change by the new value instead of the original
- Taking 20% off the sale price to reverse a discount
- Adding percentages of successive changes (a 10% rise then 10% fall is not zero change)
Key concepts
Important terms
- Multiplier
- The decimal you multiply by to apply a percentage change.
- Percentage change
- The change in a value expressed as a percentage of the original value.
- Reverse percentage
- Finding the original amount before a percentage change.
Worked examples
Problem
A jacket costs ₹1,200 after a 20% discount. What was the original price?
- 1. A 20% discount means you pay 80% of the original
- 2. The multiplier is 0.8
- 3. Original = 1200 ÷ 0.8
Answer: ₹1,500
Quick revision
- Percent = out of 100
- x% of A = A × x/100
- Change ÷ original × 100
- Increase by r%: ×(1 + r/100)
- Decrease by r%: ×(1 − r/100)
- Reverse: divide by the multiplier
Check your understanding
Question 1 · Multiple choice
What is 15% of 80?
Question 2 · Short answer
A price rises from 50 to 60. What is the percentage increase?
Question 3 · True or false
Increasing by 10% then decreasing by 10% returns you to the original amount.
Done with Percentages?
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