# Increasing and decreasing by a percentage

**There are two methods to increase an amount by a given percentage.**

The value of Matt’s house has gone up by 20% in three years. If the house was worth £180 000 three years ago, how much is it worth now?

### Method 1

Work out 20% of £180 000 and then add this to the original amount.

The amount of the increase = 20% of $180,000

= 0.2 × $180,000

= $36,000

The new value = $180,000 + $36,000

= $216,000

### Method 2

If the actual value of the increase is not known it can be deduced using a single calculation.

The first step is to add on 20%, to the 100% which gives 120% of the original amount. Calculating 120% of the original amount is equal to finding 20% and adding it to 100%.

Therefore, to increase £180 000 by 20%, calculate 120% of £180,000.

120% of £150,000 = 1.2 × £180,000

= £216,000

When converting (100 + *x*)% into a decimal multiplier, we have to divide (100 + *x*) by 100. This is usually done mentally.

**There are two methods to decrease an amount by a given percentage.**

Calculating the decrease by a given percentage is similar to working out the increase but in the opposite way. Again, there are two methods.

An iPod originally costing £110 is reduced by 30% in a sale. What is the sale price?

### Method 1

We can work out 30% of £110 and then subtract this from the original amount.

The amount taken off = 30% of £110

= 0.3 × £110

= £33

The sale price = £110 – £33

= £77

### Method 2

Method 2 calculates the percentage decrease using a single calculation.

The original amount is represented as 100%, therefore 30% is subtracted to 100% to get 70% of the original amount.

To decrease £110 by 30% we need to find 70% of £110.

70% of £110 = 0.7 × £110

= £77

Therefore, when given an amount (100%) and you decrease it by *x*%, then you will end up with

(100 – *x*)% of the original amount.

To convert (100 – *x*)% to a decimal multiplier we have to divide (100 – *x*) by 100. This is usually done mentally.