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’.

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.

- divide - to calculate what one part is worth
- multiply - to calculate the new quantity

Amount of rice required per person: 200*g* ÷ 4 = 50*g* per person

So for 6 people, I will require: 6 × 50*g* = 300*g*

Sometimes we may want to share out a quantity in a ratio. To do this

- add up the total number of parts
- calculate what one part is worth
- calculate what each person will receive
- check your calculation is correct by making sure all the parts add up to the total

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 total we have 7 + 3 = 10 parts
- So one part is worth £10,000 ÷ 10 = £1,000
- Uncle Joe’s daughter will receive 7 × £1,000 = £7,000. Uncle Joe’s grandson will receive 3 × £1,000 = £3,000.
- Check that the money the daughter and grandson receive adds up to total amount left by Uncle Joe. £7,000 + £3,000 = £10,000

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 |

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.

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?

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?

A photo measuring 4” × 6” is to be enlarged in the ratio 5:2. What size will the new photo be?

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?