Working with Proportion | Mathematics for GCSE/IGCSE - Year 11 PDF Download

Working with Proportion

There are various scenarios, like in recipes, where quantities require scaling either 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 results in the other being multiplied by the same scale factor. 
  • For instance, if 4 muffins need 100 grams of flour, then 12 muffins will require 300 grams of flour (by using a scale factor of 3). 
  • This calculation can also be represented in equivalent ratios: 4 muffins to 100 grams becomes 12 muffins to 300 grams.

What is the unitary method?

• The unitary method involves finding out the relationship of just 1 unit of a quantity. This helps us find any proportional amount easily.
• This process is used when two quantities in proportion are divided by the same scale factor.
• This concept helps determine the value of one unit of a quantity.
  • This is helpful to find 1 unit of a quantity
  • For instance, if 6 identical bicycles weigh 108 kg collectively, then one bicycle's weight is 108 ÷ 6 = 18 kg (by dividing both quantities by a scale factor of 6). 
    • Consequently, 11 bicycles would weigh 11 × 18 = 198 kg, and so forth.

How do I calculate quantities that are inversely proportional?

• When two quantities are inversely proportional, 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).
  • For example, if 200 builders can construct a stadium in 12 months, doubling the number of builders to 400 will reduce the construction time by half to 6 months.