Basic Percentages (Edexcel IGCSE Maths)

Spec point — 1.6B

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

  • $1 \frac{1}{2} = \frac{50}{100} = 50 \%$
  • $\frac{2}{5} = \frac{40}{100} = 40 \%$
  • $\frac{3}{4} = \frac{75}{100} = 75 \%$
  • The three percentages are much easier to compare than the three fractions

• Percentages are also equivalent to decimals

  • $\begin{gathered} 100 \% & = 1 \\ 10 \% & = 0.1 \\ 1 \% & = 0.01 \\ 0.1 \% & = 0.001 \end{gathered}$
  • $\begin{gathered} 25 \% & = 0.25 \\ 2.5 \% & = 0.025 \\ 0.25 \% & = 0.0025 \end{gathered}$

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

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

• Percentages can be found using 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 else can I find a percentage of an amount?

• 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 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

Worked Example Shade 35% of the grid below.

Answer:

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

Worked Example 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.

Answer:

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)

Final answer: 12.5 %