Using Ratios and Proportion

Below is additional guidance on using ratios and proportions including how to share quantities using ratio and how to find unitary ratio. There are also tips on working with ratios when different units are used.

Unitary ratios ( 1 to ? or ? to 1)

When one side of a ratio is 1 then the ratio is known as a unitary ratio. This is useful when comparing. e.g. knowing there are 3.5 times as many boys as there are girls can be more useful than knowing that the ratio of boys to girls is 7 to 2.

The table below shows how to get unitary ratios by dividing both sides by whatever the number is on the side you want to be 1.

Ratio 1 : n n : 1
3 : 4 3 ÷ 3 = 1
4 ÷ 3 = 1.33
1 : 1.33 3 ÷ 4 = .75
4 ÷ 4 = 1
.75 : 1
12 : 50 12 ÷ 12 = 1
50 ÷ 12 = 4.17
1 : 4.17 12 ÷ 50 = .24
50 ÷ 50 = 1
.24 : 1
5 : 8 5 ÷ 5 = 1
8 ÷ 5 = 1.6
1 : 1.6 5 ÷ 8 = .63
8 ÷ 8 = 1
.63 : 1

Watch out for fraction questions

Ratios can be written using fractional notation. Looking again at our purple paint example with its. 4/3 ratio of blue to red paint, if the question "what fraction of the mixture is red paint?" was asked then we would need to find how many parts are in the whole mixture.

What fraction of the mixture is red paint?

How many parts are there in total? 3 + 4 = 7
How many parts are red 3
3/7 of the mixture is red

....and watch the units too!

Keep an eye open for the units. If one quantity or amount is given in a different unit you will need to convert one or the other so both units are the same as shown in the example below.

1 liter of milk is mixed with 500 milliliters of water. What is the ratio of milk to water?

Convert one of the units. Let's convert milliliters to liters. 500 ml = .5L
Ratio = 1 : .5
Multiply both sides by 2 to get ratio = 2 : 1
Ratio of milk to water is 2 : 1

Ratios for more than two things

Ratios can also be used to show the relationship between more than two things. The ratio below shows an example of this.

A recipe for Banana Loaf calls for 8 oz. self raising flour, 5 oz. caster sugar, and 4 oz. soft margarine. The ratio of flour to sugar to margarine would be 8:5:4

Sharing with ratios

The two examples below show how we can think of shares when solving certain ratio problems.

Sally and Jo were paid $100 for doing yard work. The ratio of hours worked by Sally to Jo were 3:2. How much should each get paid?

How many shares are there in a 3:2 ratio? 3 + 2 = 5
How much were they paid for each share? $100 ÷ 5 = $20
How many shares does Sally get and how much does she get paid?

3 shares

3 x $20 = $60

How many shares does Jo get and how much does she get paid?

2 shares

2 x $20 = $40

We can check to make sure the two amounts add up to the whole $100.
($60 + $40 = $100)

 

Alex, Bill, and Chris agreed to share any lottery prize they won in a ratio of 5:3:2 (Alex to Bill to Chris). They won $50,000. How much did each get?

How many shares are there in a 5:3:2 ratio? 5 + 3 + 2 = 10
How much is each share worth?

$50,000 ÷ 10 = $5,000

How many shares does Alex get and how much money does he get?

5 shares

5 x $5,000 = $25,000

How many shares does Bill get and how much money does he get?

3 shares

3 x $5,000 = $15,000

How many shares does Chris get and how much money does he get?

2 shares

2 x $5,000 = $10,000

We can check to make sure the three amounts add up to $50,000.
($25,000 + $15,000 + $10,000 = $50,000)

 

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