Percentages of Amounts (Edexcel GCSE Maths): Revision Note

Naomi C

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Naomi C

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Percentages of Amounts

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%, 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

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

    • 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

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 7 over 20

    • This is equivalent to 0.35 or 35 over 100

    • So 7 is 35% of 20

Worked Example

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

Grid of 5x6 squares; the leftmost 2x3 section is shaded dark green, while the remaining squares are white.

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.
 

Write 150 as a fraction of 1200

150 over 1200 

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

150 over 1200 equals 0.125

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

12.5 %

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Naomi C

Author: Naomi C

Expertise: Maths

Naomi graduated from Durham University in 2007 with a Masters degree in Civil Engineering. She has taught Mathematics in the UK, Malaysia and Switzerland covering GCSE, IGCSE, A-Level and IB. She particularly enjoys applying Mathematics to real life and endeavours to bring creativity to the content she creates.