Basic Percentages (Cambridge O Level Maths)

What is a percentage?

• “Per-cent” simply means “ ÷ 100” (or “out of 100”)
• You can think of a percentage as a standardised way of expressing a fraction – by always expressing it “out of 100”
• That means it is a useful way of comparing fractions e.g.

½ = = 50% 

⅖ =  = 40%

¾ =  = 75%

How do I shade a percentage on a diagram?

• Method 1: Turn a % into a fraction then divide by the denominator and multiply by the numerator
  • To shade 60% of a grid of 20 squares...
    
    • change 60% into a fraction,
    • divide 20 squares by 5 (the denominator) to get 4 squares
    • then multiply this amount by 3 (the numerator) to get 12 squares - this is how many to shade
  • To shade 25% of a circle...
    • change 25% into a fraction, 
    • divide the circle into four quarters (dividing by the denominator, 4)
    • then shade one of these quarters
• Method 2: Turn a % into a decimal then multiply by this decimal
  • To shade 60% of a grid of 20 squares...
    
    • change 60% into a decimal, 0.6
    • then multiply 0.6 by 20 to get 0.6 × 20 = 12 squares - this is how many to shade

 How do I work out basic percentages of amounts?

• You can use simple equivalences to calculate percentages of amounts without a calculator
  • 50% =  so you can divide by 2
  • 25% = so you can divide by 4
  • 20% =  so you can divide by 5
  • 10% =  so you can divide by 10
  • 5% = so you can find 10% then divide by 2
  • 1% =  so you can divide by 100 etc.

• You can then build up more complicated percentages such as 17% = 10% + 5% + 2 x 1%

How do I find any percentage of an amount?

• Method 1: You can find any percentage of an amount by dividing by 100 and multiplying by the given %
  • 23% of 40 is 40 ÷ 100 = 0.4, multiply by 23:  0.4 × 23 = 9.2
• Method 2: To find “a percentage of X”: multiply X by the "decimal equivalent" of that percentage (percentage ÷ 100)
  • for example,  23% of 40 is 40 x 0.23 = 9.2
• To find “A as a percentage of B”: do A ÷ B to get a decimal, then x 100
  • for example, to find 26 as a percentage of 40 first do 26 ÷ 40 = 0.65, then x 100 to get 65%
    • 26 is 65% of 40