RATIO
A ratio shows how much of one thing there is compared to another. Ratios are usually written in the
form a : b. If you are making orange squash and you mix one part orange to four parts water, then the
ratio of orange to water will be 1 : 4 (1 to 4). The order in which a ratio is stated is important. You can
find equivalent ratios by multiplying or dividing by the same number as seen in the example below.
To write a ratio in its simplest form you can use the
same technique that is used to simplify fractions. You
simplify ratios by dividing the number on each side by
their highest common factor (HCF). For this example
the HCF of 2 and 6 is 2, so 2 / 2 = 1 and 6 / 2 = 3,
therefore the simplest form of the ratio 2 : 6 is 1 : 3.
Worked example (Grade 4)
There are some oranges and apples in a box.
The total number of oranges and apples is 54.
The ratio of the number of oranges to the number
of apples is 1 : 5. Work out the number of apples
in the box.
To divide a quantity in a given ratio:
1+5=6
3. Multiply your answer by each part of the
ratio. Apples come after oranges in the
sentence so use the second number in the
ratio.
54 / 6 = 9
5 x 9 = 45 apples
Worked example (Grade 5)
Jimmy is preparing the ingredients for a pizza. He
uses cheese, topping, and dough in the ratio
2 : 3 : 5. He uses 70 grams of dough. How many
grams of topping will Jimmy use?
1 part: 70g / 5 = 14g
1. Work out the number of parts in the ratio.
2. Divide the quantity by this amount.
cheese : topping : dough
2
:
3
: 5
?
:
?
: 70g
Use 5 parts = 70g to work out the weight of 1
part.
Multiply by 3 to find the weight of the topping
used.
3 parts: 3 x 14g = 42g of topping
1. There are 10 girls and 15 boys in a class. What is the ratio of girls to boys in its simplest form?
2. Simplify these ratios to their simplest forms:
a) 45 : 75 _______________________________________________________________________
b) 63 : 108 ______________________________________________________________________
c) 120 : 180 : 600 _________________________________________________________________
3. Tom and Jerry share Haribo in the ratio 2 : 3. How many do they each get if they have:
a) 20 Haribo
b) 30 Haribo
c) 55 Haribo
4. Sue, Linda, and Jo share some money in the ratio 1 : 2 : 3. How much do they get if they share:
a) £60
b) £72
c) £300