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Percentage Increase


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.



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=0.110 ÷ 100 = 0.1

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

$100x0.1=$10.\$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=0.220 ÷ 100 = 0.2

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

$80x0.2=$16\$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.


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
3121=1031 - 21 = 10
To find what percentage 10 is of 21, we need to divide
1021=0.476\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:
0.4760.476 = KaTeX parse error: Expected 'EOF', got '%' at position 5: 47.6%̲

Percentage Increase Worksheets (PDF)