3. Ratio
A ratio is something we use to compare how much there is of one thing to how much there is of another.
A ratio is written like 2:5 and is spoken as “2 to 5”. This means that for every 2 lots of one thing, there must
be 5 lots of the other.
Simplifying Ratios
To simplify a ratio, divide each part of the ratio by the same number each time, until
they can no longer be divided.
Example: Write the ration 18:60:24 in its simplest form.
We can divide each number by 3 and then by 22 (or just by 6)
This cannot be simplified anymore to make whole numbers, so the ratio is in its simplest form, which 3:10:4
5. PRACTICE QUESTION:
Olive makes her tea by adding 1 part milk to 7 parts hot water (1:7). If Olive uses 30 ml of milk, how much hot
water does she use?
6. You can use ratios to calculate total amounts, using the following steps:
Step 1: Calculate the value of one part (you may be given this in the question).
Step 2: Calculate the total number of parts.
Step 3: Calculate the total amount, by multiplying the value of one part by the total number of parts.
Example: A basic dough is made by mixing 3 parts of Greek yoghurt and 4 parts self-raising flour.
160 g of self-raising flour is used. How much dough is made in total?
4 parts self-raising flour is 160 g, so
1 part=160÷4=40 g
The total number of parts is
3+4=7
So, the total amount of dough made is 7×40g = 280 g
Practice Question:
Adam, Ben and Charlie are three brothers. The brother’s ages added together is 63. The ratio of their ages
is 3:4:2. How old is each brother?
8. Proportion
Two quantities are proportional if, as one changes, the other changes in a certain way.
We will explain direct proportion and inverse proportion.
Direct Proportion
Two quantities are directly proportional if as one increases, the other one increases at the same rate, e.g. as
one is doubled, the other is doubled.
Example: Toni uses 150 g of chocolate to make 6 cookies. How much chocolate would Toni need to
make 20 cookies?
Step 1: Divide the amount of chocolate by 6 to find the amount needed for 1 cookie.
150÷6=25 g of chocolate
Step 2: Multiply the amount of chocolate needed for 1 cookie by the 20 cookies needed.
20×25=500 g of chocolate
Inverse Proportion
Two quantities are inversely proportional if as one increases, the other one decreases at the same rate, e.g.
as one is doubled, the other is halved.
Example: It takes 8 workers 25 months to build 10 houses. Assuming they all work at the same rate, how long
would it take 20 workers to build the same number of houses?
Step 1: Multiply the number of workers by the number of months, to find the time it would take 1 worker to
build 10 houses:
8×25=200 months
Step 2: Divide the time it takes 1 worker to build 10 houses by 20 workers, to get the answer:
200÷20=10 months
