Text
Unit A3 Section 1
Simple Ratios

Ratios are used in many situations to describe how two quantities are related. For example, a cake recipe requires twice as much flour as margarine. The ratio of flour to margarine is 2 : 1. Sometimes ratios can be simplified; for example, the ratio 100 : 50 is the same as the ratio 2 : 1. Ratios are simplified in a very similar way to fractions.

Worked Examples

1

Simplify each of the following ratios.

(a)
48 : 12

Both numbers in the ratio can be divided by 12. This gives

48 : 12 = 4 : 1

Alternatively, the ratio can be simplified in a number of steps.

48 : 12 = 24 : 6
= 12 : 3
= 4 : 1
(b)
27 : 9

Here both numbers in the ratio can be divided by 9. This gives

27 : 9 = 3 : 1

Alternatively, the ratio can be simplified in steps to give

27 : 9 = 9 : 3
= 3 : 1
(c)
35 : 49

Here both numbers can be divided by 7 to give

35 : 49 = 5 : 7
2

A school class contains 12 girls and 20 boys. Find the ratio of:

(a)
girls to boys,

The ratio of girls to boys is:

12 to 20 or 12 : 20

This can be simplified by dividing both numbers by 4, to give

12 : 20 = 3 : 5
(b)
boys to girls.

To find the ratio of boys to girls, reverse the ratio of girls to boys, to give 5 : 3.
3

A glass contains 300 cm3 of drink. The drink is made by mixing 50 cm3 of concentrate with water. Find the ratio of concentrate to water.

Amount of water = 300 − 50
= 250 cm3

The ratio of concentrate to water is

50 : 250

which simplifies to

1 : 5
4

The ratio of blue sweets to other coloured sweets in one packet is 1 : 12. How many sweets would there be in the packet if it contained:

The ratio of 1 : 12 means that for every blue sweet there are 12 sweets of other colours.

(a)
3 blue sweets?

This packet contains 3 blue sweets and 3 × 12 = 36 other sweets.

In total the packet contains 3 + 36 = 39 sweets.
(b)
5 blue sweets?

This packet contains 5 blue sweets and 5 × 12 = 60 other sweets.

This give a total of 65 sweets.

Challenge!

A cashier of a bank was given one million one cent coins to count. How long will he take if he can count five coins in one second?

Exercises

Simplify each of the following ratios.

(a)
4 : 2 :
(b)
8 : 2 :
(c)
3 : 6 :
(d)
9 : 12 :
(e)
5 : 30 :
(f)
8 : 42 :
(g)
3 : 18 :
(h)
25 : 75 :
(i)
8 : 100 :
(j)
30 : 240 :
(k)
64 : 80 :
(l)
21 : 15 :
(m)
81 : 48 :
(n)
32 : 100 :
(o)
50 : 49 :
(p)
4.8 : 1.2 :
(q)
10.5 : 3.5 :
(r)
8.6 : 30.1 :

A school contains 300 girls and 320 boys. Find:

(a)
the ratio of girls to boys, :
(b)
the ratio of boys to girls. :

The shape of a room is a rectangle with sides of length 5 m and 3.5 m. Find the ratio of:

(a)
the length to the width, :
(b)
the width to the length. :

Two different bus companies have different pricing policies.

For Company A on one route the adult fare is £1.20 and the child fare is 40 p.

For Company B on a different route, the adult fare is £1.40 and the child fare is 70 p.

(a)

Find the ratio of the child fare to the adult fare for each company.

Company A :

Company B :

(b)

Which company gives children the better deal?

Orange syrup is mixed with water in the ratio 1 : 8, that is, 1 part orange syrup to 8 parts water. How much water is mixed with:

(a)
100 cm3 of syrup, cm3
(b)
20 cm3 of syrup, cm3
(c)
5 cm3 of syrup? cm3

In a school the ratio of teachers to students is 1 : 20. If there are 12 teachers, how many students are there in the school?

students