Basic Percentages (WJEC GCSE Maths & Numeracy (Double Award): Foundation): Revision Note

Basic percentages

What is a percentage?

• “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. $\frac{234}{650}=234÷650=0.36=36\%$

How do I find a percentage of an amount without a calculator?

• There are some percentages of an amount that are easy to work out

  • To find 50%, halve the amount

  • To find 25%, halve 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

How do I find a percentage of an amount with a calculator?

• 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

  • Write 12% as a decimal multiplier

    • 12% is equivalent to 0.12

  • 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

How do I express one number as a percentage of another?

• 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