Percentage decrease for beginners
Explore reductions using discounts and simple contexts.
Quick answer
Percentage decrease means finding how much something has gone down in size, value, or amount, shown as a part of 100. For example, if a toy that costs £10 goes down to £8, it has decreased by 20%.
Learning outcome
By the end of this page, you will be able to find the percentage decrease when something gets smaller, using simple steps and real-life examples.
- You can calculate how much a price drops in percentage terms
- You can use a simple formula to find percentage decrease
- You can solve word problems involving percentage decrease
- You can check your answers using a different method
Why this matters
Knowing how to find percentage decrease helps you understand how prices change in shops, how discounts work, and how much things get smaller or less. It’s useful for shopping, saving money, and making smart choices. It also helps with more advanced maths later, like compound interest and growth.
How it works
Percentage decrease is about finding the difference between a starting amount and a new, smaller amount. Then, you work out what that difference is as a part of 100.
- Find the original amount and the new amount
- Subtract the new amount from the original amount
- Divide the difference by the original amount
- Multiply the result by 100 to get the percentage
Examples you can see
Let’s imagine you have a bag of 20 sweets, and you eat 5 of them. That means you have 15 sweets left. What percentage of your sweets did you eat?
| Step | What you do | Calculation |
|---|---|---|
| 1 | Find original amount | 20 sweets |
| 2 | Find new amount | 15 sweets |
| 3 | Find the difference | 20 – 15 = 5 sweets |
| 4 | Divide difference by original | 5 ÷ 20 = 0.25 |
| 5 | Multiply by 100 | 0.25 × 100 = 25% |
You ate 25% of your sweets!
Let’s try another one with money. A toy costs £30, but it is now £24. What is the percentage decrease?
| Step | What you do | Calculation |
|---|---|---|
| 1 | Find original price | £30 |
| 2 | Find new price | £24 |
| 3 | Find the difference | £30 – £24 = £6 |
| 4 | Divide difference by original | £6 ÷ £30 = 0.2 |
| 5 | Multiply by 100 | 0.2 × 100 = 20% |
The price went down by 20%.
Try it as a mini adventure
Imagine you are a shop owner and you have a big sale! You start with 100 toys in your shop. At the end of the sale, only 70 toys are left. You want to tell your customers how much the number of toys has decreased.
- Original number of toys = 100
- New number of toys = 70
- Difference = 100 – 70 = 30 toys
- Percentage decrease = (30 ÷ 100) × 100 = 30%
Great job! You told your customers that 30% of your toys were sold during the sale!
Common mistakes
- Mistake: Using the new number instead of the original number in the formula.
- Why it happens: Confusing which number to divide by.
- Fix: Always divide the difference by the original amount, not the new amount.
- Mistake: Forgetting to multiply by 100 to get the percentage.
- Why it happens: Thinking that decimals are already percentages.
- Fix: Remember that decimals must be multiplied by 100 to become percentages.
- Mistake: Not subtracting the new amount from the original amount.
- Why it happens: Not understanding that we need the size of the decrease.
- Fix: Always subtract new from original to find how much it went down.
Parent and carer guide
Helping your child with percentage decrease can be fun and simple. Here’s how to get started:
- Start with real-life examples: Use a shopping receipt, a sale on toys, or a price drop on a favourite snack.
- Use visual aids: Draw bar models or use blocks to show the original and new amounts.
- Practice with small numbers: Begin with simple examples like 20 to 15, or £10 to £8.
- Check together: Ask your child to double-check their work by using the reverse calculation.
- Keep it light: Don’t push too hard. If they get stuck, take a break and try again later.
Remember: it’s okay if they don’t get it right away. The goal is to understand the idea, not to be perfect.
Practice questions
- Original amount = 50, New amount = 35. What is the percentage decrease?
- Original price = £40, New price = £32. What is the percentage decrease?
- Original number = 80, New number = 60. What is the percentage decrease?
- Original amount = 100, New amount = 75. What is the percentage decrease?
- Original price = £60, New price = £48. What is the percentage decrease?
Answers:
- (50 – 35) ÷ 50 × 100 = 30%
- (40 – 32) ÷ 40 × 100 = 20%
- (80 – 60) ÷ 80 × 100 = 25%
- (100 – 75) ÷ 100 × 100 = 25%
- (60 – 48) ÷ 60 × 100 = 20%
FAQ
What does percentage decrease mean?
Percentage decrease means how much something has gone down in size or value, shown as a part of 100.
How do I find percentage decrease?
Subtract the new amount from the original amount, divide by the original amount, and multiply by 100.
Why do we use percentage decrease?
We use it to understand how much prices, sizes, or amounts have changed in a clear and useful way.
Can percentage decrease be more than 100%?
No, because that would mean it went down more than it originally was. For example, if you had 10 sweets and ate 15, you couldn’t have eaten more than you had!
Is percentage decrease the same as percentage change?
Not exactly. Percentage decrease only looks at how much something went down. Percentage change looks at both increases and decreases.