- To find 10%, divide a number by 10.
- The original mass of chocolate is 200 grams.
- 200 ÷ 10 = 10 and so 10% of 200 grams in 20 grams.
- To increase an amount by 10%, add 10% to the original amount.
- 200 + 20 = 220. Therefore the new mass is 220 grams
Subtract the percentage from the original amount to decrease by a percentage.
- To find 40%, first find 10% and then multiply it by 4.
- 10% is found by dividing the number by 10. £50 ÷ 10 = £5 and so, 10% is £5.
- We multiply 10% by 4 to get 40%. £5 × 4 = £20 and so, 40% is £20.
- In a sale, the price is decreased.
- To decrease by a percentage, subtract the percentage from the original number.
- £50 – £20 = £30 and so, the new price is £30.
Percentage Change Word Problems
How to Work out Percentage Change
To work out percentage change, follow these steps:
- Work out the percentage by dividing the original number by 100 and multiplying by the percentage.
- For a percentage increase, add this percentage to the original number.
- For a percentage decrease, subtract this percentage from the original number.
For example, in this percentage change question, we will increase $52 by 23%.
Step 1 is to find the percentage.
To find 23%, divide $52 by 100 and then multiply by 23.
$52 ÷ 100 × 23 = $11.96. Therefore 23% of $52 is $11.96
We are going to increase the value by 23%.
Step 2 is to add the percentage to the original number.
$52 + $11.96 = $63.96. Therefore $52 increased by 23% is $63.96
Here is another example with percentage decrease. We will decrease $75 by 36%.
The first step is to find the percentage by dividing the amount by 100 and multiplying by the percentage.
$75 ÷ 100 × 36 = 27. Therefore 36% of $75 is $27.
This is a percentage decrease question.
The next step is to subtract the percentage from the original amount.
Here are some common percentages that can be found without a calculator:
- To find 1%, divide by 100.
- To find 5%, divide by 20.
- To find 10%, divide by 10.
- To find 20%, divide by 5.
- To find 25%, divide by 4.
- To find 50%, divide by 2.
Percentage Increase Word Problems
Here is a real life example of word problems involving percentage increase.
In this example, we increase the mass of a bar of chocolate by 10%
The first step is to work out the percentage value. We want to find 10%.
To find 10% of a number, divide it by 10.
10% of 200 grams is 20 grams.
This is a percentage increase word problem, so we add the percentage to the initial amount.
200 + 20 = 220 and so, the new mass of chocolate is 220 g.
Percentage Decrease Word Problems
Here is a real life example of word problems involving percentage decrease.
This is a percentage decrease problem because we want to find the new price of the item after it has gone on sale. A sale means that the price has gone down.
The first step is to find the percentage value.
40% is found by finding 10% and multiplying this by 4.
10% is £5 because £50 divided by 10 = £5.
We multiply 10% by 4 to find 40%. 40% is £20.
This is a percentage decrease question because we want to take 40% off the total price.
In a percentage decrease problem, subtract the percentage from the original amount.
£50 – £20 = £30 and so the sale price is £30.
Now try our lesson on Converting Percentages to Fractions where we learn how to write a percentage as a fraction.