A ratio is a comparison between two or more values, usually written with a colon between the values. For example, we would read the ratio 3:4 as ‘three to four’.
Suppose a certain shade of grey paint is made by mixing 3 parts black paint with 4 parts white paint, then the black and white paint are mixed in the ratio 3:4. If we were asked what the ratio of white to black paint was, we would have to say 4:3. So it is important that we get our ratio the right way round.
To make a comparison between information given in the form of ratios, we can calculate unit amounts, or in other words, find out what one part is worth.
My favourite teabags come in boxes of 48 or 80. The box containing 48 teabags costs £1.20 whilst the box containing 80 teabags costs £1.92. Which box is better value?
How do we compare prices? We find the cost (pence) per teabag for each box.
Small box: 120p ÷ 48 = 2.5p per teabag
Large box: 192p ÷ 80 = 2.4p per teabag
The cost per teabag is less for the larger box, so this is better value.
To simplify a ratio, divide through each term by a number which divides into both.
Both numbers can be divided by three, so the ratio could be written as 3:4.
Amount of rice required per person: 200g ÷ 4 = 50g per person
So for 6 people, I will require: 6 × 50g = 300g
Sometimes we may want to share out a quantity in a ratio. To do this
In his will Uncle Joe has left his savings of £10,000 to be split between his daughter and grandson in the ratio 7:3. How much money will each receive?
In a bag I have 8 black balls and 3 red. What is the ratio of red to black balls?
Which of the following bottles of water is the cheapest?
|Welsh Wizard||Irish Mist||Eau Francais||Scotch Broth|
|£1.62 for 2 litres||£3.20 for 4 litres||£1.35 for 0.5 litres||£4.48 for 7 litres|
Calculate the cost in pence per litre.
Welsh Wizard: 162p for 2 litres = 162 ÷ 2 = 81p per litre
Irish Mist: 320p for 4 litres = 320 ÷ 4 = 80p per litre
Eau Francais: 135p for 0.5 litres = 135 ÷ 0.5 = 270p per litre
Scotch Broth: 448p for 7 litres = 448 ÷ 7 = 64p per litre
Write the ratio 21:49 in its simplest form.
A chocolate bar is made up of 40 pieces. Alex ate 20 pieces, Bernard 16 pieces and Charles 4 pieces. Express this as a ratio in its simplest terms.
The ratio is 20:16:4
Each of these values is divisible by 4, so in its simplest terms, the ratio can be written as 5:4:1.
A mixture used to make concrete contains 1 part cement, 2 parts sand, and 4 parts gravel. If 6 bags of sand are used, how many bags of cement and gravel are used?
The ratio of parts to bags is 2 parts : 6 bags
In simpler terms we could write this as 1 part : 3 bags
We require 1 part in the ratio 1 part : 3 bags, so 3 bags
We require 4 parts in the ratio 1 part : 3 bags, so 12 bags
One hundred and thirty-five pounds is to be divided up between Alex, Bernard and Charles in the ratio 3:2:4. How much will each receive?
There are 3+2+4 = 9 parts in total
One part will be worth £135 / 9 = £15
Alex will get 3 × £15 = £45
Bernard will get 2 × £15 = £30
Charles will get 4 × £15 = £60
Check: Do these amounts add up to £135?
Total = £45 + £30 + £60 = £135
A photo measuring 4” × 6” is to be enlarged in the ratio 5:2. What size will the new photo be?
Firstly, divide 4” by 2 to get one unit, i.e. 2”
Then multiply by 5 to get the new width, i.e. 2” × 5 = 10”
Firstly, divide 6” by 2 to get one unit, i.e. 3”
Then multiply by 5 to get the new width, i.e. 3” × 5 = 15”
I would like to reduce the size of a poster in the ratio 12 : 7. The size of the original is 60cm × 84cm. What will the size of the new poster be?
Firstly, divide by 12 to get one unit, i.e. 60cm ÷ 12 = 5cm
Then multiply by 7 to get the new width, i.e. 5cm × 7 = 35cm
Firstly, divide by 12 to get one unit, i.e. 84cm ÷ 12 = 7cm
Then multiply by 7 to get the new width, i.e. 7cm × 7 = 49cm