Working with Proportion
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
Examiner Tip
Read the question to see if your answer needs to be a whole number
- For example, the number of servings in a recipe should be a whole number
- You might have to decide which way to round when working with actual objects
- this might not always be the same way that you would normally round a number
- e.g. if you end up needing 1.2 bags of flour you'd have to round up and buy 2 bags to have enough!
- or if you have enough flour to make 12.9 pancakes, that's still only enough to make 12 whole pancakes
Worked example
The ingredients for 12 cookies are as follows:
90 g butter
130 g chocolate
180 g flour
150 g sugar
1 egg
(a) If Tanya makes 50 cookies, how much sugar does she need?
12 cookies require 150 g of sugar
Find how much sugar is needed to make 1 cookie (by dividing 150 by 12)
150 ÷ 12 = 12.5 grams of sugar for 1 cookie
Find how much sugar is needed for 50 cookies (by multiplying 12.5 by 50)
12.5 × 50 = 625
625 grams of sugar
(b) If Giles buys a 500 gram bag of flour to make cookies, how many whole cookies can he make?
Method 1
12 cookies require 180 g of flour
Find out how much flour is in 1 cookie (by dividing 180 by 12)
180 ÷ 12 = 15 grams of flour for 1 cookie
Find how many lots of 15 grams are in 500 grams of flour (by dividing 500 by 15)
500 ÷ 15 = 33.33… cookies
Write down how many whole cookies can be made
There is not enough for 34 whole cookies
33 cookies
Method 2
12 cookies have 180 grams of flour
Find how many lots of 12 cookies the 500-gram bag of flour contains (by dividing 500 by 180)
500 ÷ 180 = 2.77… lots of 12 cookies
Calculate how many cookies are in 2.77… lots of 12 cookies (by multiplying 2.77… by 12)
2.77… × 12 = 33.33… cookies
Write down how many whole cookies can be made
There is not enough for 34 whole cookies
33 cookies
