Basic Percentages | Mathematics for GCSE/IGCSE - Year 11 PDF Download

What is a percentage?

• "Percent" simply means "divided by 100" (or "out of 100"). 
• You can think of a percentage as a standardized way of expressing a fraction – always expressed out of 100. 
• This makes it useful for comparing fractions. For example:
  

How do I work out basic percentages of amounts?

• You can use simple equivalences to calculate percentages without a calculator:
  • 50% = 1/2 Divide the number by 2
  • 25% = 1/4 Divide the number by 4
  • 20% = 1/5 Divide the number by 5
  • 10% = 1/10 Divide the number by 10
  • 5% = 1/20 Find 10%, then divide by 2
  • 1% = 1/100 Divide the number by 100, and so on
• Building Up Complex Percentages: 17% = 10% + 5% + 2 * 1%

How do I find any percentage of an amount?

• Method 1: You can calculate any percentage of an amount by dividing the amount by 100 and then multiplying by the given percentage.
  • Example: To find 23% of 40, calculate 40 ÷ 100 = 0.4, then 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).
  • Example: 23% of 40 is calculated as 40 * 0.23 = 9.2
• To find "A as a percentage of B": Divide A by B to get a decimal, then multiply by 100.
  • Example: To find 26 as a percentage of 40, first calculate 26 ÷ 40 = 0.65, then multiply by 100 to get 65%. Therefore, 26 is 65% of 40.