Academic Skills Advice
Percentages Summary
Percent means per hundred.
For example: 35% means 35 per hundred. It can also be written as
or 0.35
Some Common Percentages:
The table shows some commonly used percentages and their equivalent decimal and
fraction. It also shows an easy way to find these percentages.
Percent
Decimal
Fraction
How to work it out.
10%
0.1
÷10
20%
0.2
÷5
25%
0.25
÷4
50%
0.5
÷2
75%
0.75
÷4 then x3
Finding a percentage of a number


Make the percent into a fraction
Multiply by the amount (you can also make the amount into a fraction by putting a 1 under it)
Find 15% of £80
Percentage Increase or Decrease

Find the percent as above then:
o Add it on for an increase
o Subtract it for a decrease
The price of a book increases by 8%. If the original price is £5 what is the new price?
so the new price is £5 + 40p = £5.40
(nb. If the question said the price decreases then you would subtract the 40p)
© H Jackson 2010 / Academic Skills
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Writing one Number as a Percentage of Another:


Make a fraction.
Multiply by 100 to turn it into a percent.
Out of a group of 25 volunteers, 20 are going abroad. What percentage is this?
(Make 20 out of 25 into a fraction then x100)
Percentage Profit or Loss:


Make a fraction (profit or loss over the original)
Multiply by 100 to turn it into a percent.
Doug bought a collection of CD’s for £50 then sold it a year later for £65. What was his
percentage profit?
=
Reverse Percentages:
Sometimes you may be given the price of an item after a percentage increase or decrease
and be asked to find the original price. This is not straightforward as you would have to find
a percentage of the original price (which you don’t know yet). The following method can be
used:


Find the new percent
Find 1% using the new price
 x100 to find the original price (100%)
An item is bought in a ‘30% off’ sale for £63. How much did the item cost originally?
The sale price is 30% less than the original price (100-30) = 70% of the original. So the new
price (£63) is 70%.
70% = £63
Find 1%:
1%
= 66 ÷ 70 = 0.9
Find 100%: 100% = 0.9 x 100 = £90
So the original price of the item was £90. (Check this is correct by finding 30% of £90 and
taking it off to make sure you find the sale price of £63.)
Notice: the original amount is always 100%.
© H Jackson 2010 / Academic Skills
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