Introduction to Ratio
What is a ratio?
- A ratio is a way of comparing one part of a whole to another
- Ratios are used to compare one part to another part
- How many parts that make the whole will depend on the question
- Ratios are used to compare one part to another part
What do ratios look like?
- Ratios involve two or three different numbers separated using a colon
- E.g., 2 : 5, 3 : 1, 4 : 2 : 3
- In all ratio questions, who or what is mentioned first in the question, will be associated with the first part of the ratio
- E.g., The cake recipe with flour and butter in the ratio 2 : 1
- 'Flour' is associated with '2' and 'butter' is associated with '1'
- E.g., The cake recipe with flour and butter in the ratio 2 : 1
- The numbers in a ratio tell us, for each quantity involved, its proportion of the whole
- In the ratio 4 : 3
- The first quantity comprises 4 parts (of the whole)
- The second quantity comprises 3 parts (of the whole)
- In total, the whole is made up of 4 + 3 = 7 parts
- In the ratio 2 : 5 : 3
- The first quantity comprises 2 parts (of the whole)
- The second quantity comprises 5 parts (of the whole)
- The third quantity comprises 3 parts (of the whole)
- In total, the whole is made up of 2 + 5 + 3 = 10 parts
- In the ratio 4 : 3
Examiner Tip
- Start by writing down any information given in words as values, and use abbreviations to refer to them.
- This will make it easier to look back at the information later
- E.g. For a flour and butter cake mix, where twice as much flour is needed as butter, you could write
Worked example
A pot of money is shared between three friends, Dave, John and Mary.
Dave receives $450, John receives $200 and Mary receives $350.
Find the total amount of money in the pot.
Add up the three separate amounts
$1000
Write down the ratio of money received by Dave, John and Mary.
(There is no need to simplify the ratio.)
Be careful with the order
Dave gets mentioned first, so 450 will be the first part of the ratio, then John and finally Mary
450 : 200 : 350
(There is no need to simplify the fraction.)
Fractions are compared to the whole, so this will be 'Mary's money' "out of" 'total money'