Simplifying ratiosA ratio is a comparison of numbers in a definite order.

The numbers are expressed in the same units and are called the terms of the ratio.

Simplified ratios contain no decimals or fractions.

A ratio can be written in the form a:b orba

If the terms of a ratio are multiplied or divided by any number (except zero) an equivalent ratio is formed.

Simplifying ratios is just like simplifying fractions, each term is multiplied or divided by the same number.

Simplify the following

a) 27:18 b) 45m2:136m2 c) 5½kg:6¼kg 9

18:

9

27

2:3

45:136

2136

:2

450×100 ×100

= 450:136

= 225:68

5½:6¼×4 ×4

= 22:25

Same units.No decimals.

You can simplify this using your calculator, BUT put the smaller term in first.REMEMBER if in the original the larger was first, write the larger first in your answer!!

Same units.No fractions.

Example 1

A saleswoman served 40 customers, 28 of which were female. What was the ratio of male to female customers?

male:female = 12:28 = 3:7

Be aware that you will often be given information about one item and asked about another, eg told about females and asked about males.

males = 40 – 28 = 12

Example 2

Simplify the following

a) 2m:18cm b) 36t:6000kg

218

:2

200

9:100

2m:18cm = 200cm:18cm 36t:6000kg = 3600kg:6000kg

12006000

:12003600

5:3

Same units

Example 3

c) 18:27:24 d) 36:6:44

HCF is 33

24:

3

27:

3

18

8:9:6

No decimals44:60:36

11:15:9

HCF is 44

44:

4

60:

4

36

Today’s work

Yesterday’s work

Exercise 4.2Page 165 168All Qs 1st column only

Exercise 4.1Page 160 163All Qs 1st column only