Working with Percentages (CIE IGCSE Maths: Extended)

How do I increase or decrease by a percentage?

• Identify “before” & “after” quantities
• If working in percentages, add to (or subtract from) 100 
  • a percentage increase of 25% is 100 + 25 = 125% of the "before" price
    • Add 25% to the original amount
  • a percentage decrease of 25% is 100 - 25 = 75% of the "before" price
    • Subtract 25% from the original amount
• A multiplier, p, is the decimal equivalent of a percentage increase or decrease
  
  • The multiplier for a percentage increase of 25% is p = 1 + 0.25 = 1.25
    • Multiply the original amount by the multiplier, 1.25, to find the new amount
  • The multiplier for a percentage decrease of 25% is p = 1 - 0.25 = 0.75
    • Multiply the original amount by the multiplier, 0.75, to find the new amount
• The amount "before" and the amount "after" a percentage change are related by the formula "before" × p = "after"
  • where p is the multiplier

How do I find a percentage change?

• Method 1: rearrange the formula "before" × p = "after" to make p (the multiplier) the subject
  • p =  
  • Calculate p and interpret its value
    • p = 1.02 shows a percentage increase of 2%
    • p = 0.97 shows a percentage decrease of 3%
• Method 2: Use the formula that the "percentage change" is  
  • A positive value is a percentage increase 
  • A negative value is a percentage decrease
• The same formula can be used for percentage profit (or loss)
  • the "cost" price is the price a shop has to pay to buy something and the "selling" price is how much the shop sells it for

• You can identify whether there is a profit or loss 
  • cost price < selling price = profit (formula gives a positive value)
  • cost price > selling price = loss (formula gives a negative value)

What is a reverse percentage?

• A reverse percentage question is one where we are given the value after a percentage increase or decrease and asked to find the value before the change

How to do reverse percentage questions

• You should think about the "before" quantity (even though it is not given in the question)
• Find the percentage change as a multiplier, p (the decimal equivalent of a percentage change)
  • a percentage increase of 4% means p = 1 + 0.04 = 1.04
  • a percentage decrease of 5% means p = 1 - 0.05 = 0.95
• Use "before" × p = "after" to write an equation
  • get the order right: the change happens to the "before", not to the "after"
• Rearrange the equation to find the "before" quantity...
  • ...by dividing the "after" quantity by the multiplier, p