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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.

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.

Examples

Carter saw a book he wanted on Amazon for \$21. The next day he noticed that the price had increased to \$31. By what percent did the price increase?
First, find the number of dollars the price increased
$31 - 21 = 10$
To find what percentage 10 is of 21, we need to divide
$\dfrac{10}{21} = 0.476$
Moving the decimal place two to the right and then putting a % sign at the end of the number we get:
$0.476$ = KaTeX parse error: Expected 'EOF', got '%' at position 5: 47.6%̲