There are many situations, such as with recipes, where quantities need to be scaled up or down.

How do I calculate quantities that are in proportion?

• If two quantities are in proportion, then multiplying one by a scale factor means the other will be multiplied by the same scale factor
  
  • E.g. if 4 muffins require 100 grams of flour then 12 muffins require 300 grams of flour (by multiplying both quantities by a scale factor of 3)
  • The working can also be written in equivalent ratios
    • 4 muffins : 100 grams becomes 12 muffins : 300 grams

What is the unitary method?

• The unitary method is when the proportion relating to just 1 unit of a quantity is found. This can be used to find any proportional amount
• This is done when two quantities in proportion are divided by the same scale factor
  
  • This is helpful to find 1 unit of a quantity
  • E.g. if 6 identical bicycles weigh 108 kg, then 1 bicycle weighs 108 ÷ 6 = 18 kg (by dividing both quantities by a scale factor of 6)
    • This means 11 bicycles weigh 11 × 18 = 198 kg etc

How do I calculate quantities that are inversely proportional?

• If two quantities are inversely proportional, then as one increases the other decreases
• Multiplying one quantity by a scale factor will divide the other quantity by the same scale factor (and vice versa)
• E.g. if 200 builders can build a stadium in 12 months, then doubling the number of builders to 400 will halve the time it takes to 6 months