Basic Percentages
‘Percent’ means ‘out of a hundred. So a percentage is just a fraction withh 100 as the denominator. This can also be turned into a decimal, like so:
17% = 17/100 = 0.17
To increase or decrease an amount by a percentage, simply calculate the percent change then add or subtract, eg:
Increase 150 by 20%
20% = 20/100
150 x 20/100 =30
150 + 30 = 180
When using money, it’s often easier to change it into pennies, then change the answer back into pounds:
Reduce £5 by 40%
£5 = 500p
500p x 40/100 = 200p
5000p - 200p = 300p = £3
Another way of doing these questions is direct multiplication. If something has gone up by 17% then the new percentage is 117%, so you multiply by 1.17 If something has gone down by 8% then the new percentage is 92%, so you multiply by 0.92. Using the example earlier:
Increase 150 by 20%
Original percent = 100%
Increase by 20% = 100 + 20 = 120%
120% = 120/100 = 1.2
150 x 1.2 = 180
Percentage Change
To find out how much something has changed as a percentage, use the equation
(change / orginal) x 100%
So if I buy something for £50 and sell it for £60, the change in price is £10. This gives:
(10/50) x 100% = 20% increase
If the amount has gone down, the change will be negative. So if something I bought for £80 is now only worth £72 then the change is negative £8. This gives:
(-8/80) x 100% = -10% = 10% decrease
Reverse Percentage
A common question in the National5 exam is reverse percentage. Here you are told the current value and how much it has changed by, then you need to ‘go back in time’ to find the original value. For example:
A club has 70 members this year. This is a 40% increase on last year. How members did the club have last year?
If you are not allowed a calculator, here’s one way of doing it:
40% increase on last year means 140% of last year
So 140% = 70
So 14% = 7
So 1% = 7/14 = 0.5
So 100% = 100 x 0.5 = 50
So the club had 50 members last year
If you have a calculator then an alternative is to work out the decimal for the percent change and divide by it instead of multiplying. Doing the same question this way:
40% increase on last year means 140% of last year
140% = 1.4
70 / 1.4 = 50
So the club had 50 members last year
Watch out for different ways of asking you to do reverse percentages. For example, the question might gice you a price after discount and ask you to work out the price before the discount. In general, if the question gives you the percentage change and the final value then you’ll be using reverse percentage.