## Percentage Increase

#### Introduction

Percentage is a scale used to compare items of different values. A percentage measures everything on the same scale, from 0 to 100. Something that is half the size of something else can be said to be 50% of the size.

If we buy tickets for a concert every year for $100, and find out that the ticket price has gone up 10%, we can quickly and easily calculate what the actual price is. If another concert sells tickets for $80 but has put their price up 20%, we can compare which of the two is cheaper.

#### Terms

## Lesson

To calculate percentage increase, we can use the percentage to work out the actual increase. The steps we need to follow are:

1) Calculate the actual increase by using the percentage

2) Add this amount back on to the original amount to find the new price

Using the examples of the concerts above:

The first concert used to sell tickets for $100 but has put them up 10% this year.

Firstly, we need to work out 10% of $100. To do this, we need to turn 10% into a decimal. To turn any percentage into a decimal, we take the percentage number and divide by 100.

So, $10 ÷ 100 = 0.1$

Now, to work out 10% of $100, we multiply the $100 by 0.1:

$\$100 x 0.1 = \$10.$

Therefore, the cost of the ticket has increased by $10. We can then add that back on to the cost of the original ticket to work out the new price:

$100 (original cost) + $10 (the increase) = $110 (the new price).

Let's try that again with the ticket for the other concert. Their old price was $80 and they have raised the cost by 20%.

Firstly, we turn 20% into a decimal by diving 20 by 100.

$20 ÷ 100 = 0.2$

Then, we multiply the old cost ($80) by 0.2:

$\$80 x 0.2 = \$16$

So, the price increase is $16. We can then add that back on to the original price to work out the new price:

$80 (original cost) + $16 (the increase) = $96 (the new price).

Therefore, the second concert is still cheaper, despite the percentage increase being higher.