Basic Percentages | Edexcel GCSE Maths: Foundation Revision Notes 2017

Introduction to Percentages

“Per-cent” simply means “out of 100” (or “ ÷ 100”)
Rewriting fractions as percentages means they can be compared more easily
You can do this by finding an equivalent fraction with a denominator of 100
- $\frac{1}{2} = \frac{50}{100} = 50 %$
- $\frac{2}{5} = \frac{40}{100} = 40 %$
- $\frac{3}{4} = \frac{75}{100} = 75 %$
- The three percentages are much easier to compare than the three fractions
Percentages are also equivalent to decimals
- $\begin{array}{rcl} 100 % & = & 1 \\ 10 % & = & 0.1 \\ 1 % & = & 0.01 \\ 0.1 % & = & 0.001 \end{array}$

- $\begin{array}{rcl} 25 % & = & 0.25 \\ 2.5 % & = & 0.025 \\ 0.25 % & = & 0.0025 \end{array}$

Notice that a decimal can be converted to a percentage by multiplying by 100
- Therefore a percentage can be converted to a decimal by dividing by 100
A fraction can be written as a percentage by finding the decimal equivalent
- You could use your calculator to do this
- e.g. $\frac{234}{650} = 234 \div 650 = 0.36 = 36 %$

There are some percentages of an amount that are easy to work out
- To find 50%, half the amount
- To find 25%, half the amount, twice (finding a quarter)
- To find 10%, divide the amount by 10
- To find 1%, divide the amount by 100
These percentages can then be used as building blocks to find other percentages, for example:
- To find 20%, find 10% and then double it
- To find 5%, find 10% and halve it
- To find 0.1%, find 1% and divide it by 10
- To find 12%, find 10% and 1%, then add together the 10% and two lots of the 1%
To find a percentage larger than 100%, remember that 100% is the original amount
- To find 150%, find 50% and add it on to the original amount

Whilst the methods above can be used with a calculator it is more efficient to use multipliers
A multiplier is the decimal equivalent of a percentage
e.g. To find 12% of 650
- 12% is equivalent to 0.12
  - This is the multiplier
- Find the product of the amount and the multiplier, using your calculator
- 0.12 × 650 = 78
- So 12% of 650 is 78
When finding a percentage larger than 100%, the multiplier will be greater than 1
- The multiplier for finding 126% of an amount would be 1.26

Start by writing one number as a fraction of the other
Find the decimal equivalent of this fraction using your calculator
- or find an equivalent fraction with a denominator of 100
Rewrite this as a percentage
e.g. To find 7 as a percentage of 20
- Write as $\frac{7}{20}$
- This is equivalent to $0.35$ or $\frac{35}{100}$
- So 7 is 35% of 20

Shade 35% of the grid below.

Count the total number of squares in the grid

Total of 40 squares

Find 35% of 40
Start by finding 10%, to help find 5% and 30%

10% of 40 = 4
so 30% of 40 = 4 × 3 = 12
and 5% of 40 = 4 ÷ 2 = 2

35% of 40 = 12 + 2 = 14

Shade 14 squares
It doesn't matter which 14 you shade

Amber owes £ 1200 for a trip. She has to pay a deposit of £ 150 to secure her place.

Express the deposit as a percentage of the price of the trip.

Write 150 as a fraction of 1200

$\frac{150}{1200}$

Find the value of this fraction as a decimal, using your calculator

$\frac{150}{1200} = 0.125$

Write this as the equivalent percentage (by multiplying by 100)

12.5 %