Simplifying ratios A 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 or 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) 27:18b) 4  5m 2 :1  36m 2 c) 5½kg:6¼kg 4  5:1  36 ×100 = 450:136 = 225:68 5½:6¼ ×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:18cmb) 3  6t:6000kg 2m:18cm = 200cm:18cm 3  6t:6000kg = 3600kg:6000kg Same units Example 3 c) 18:27:24d) 3  6:6:4  4 HCF is 3 No decimals HCF is 4

Today’s work Yesterday’s work Exercise 4.2 Page 165  168 All Qs 1 st column only Exercise 4.1 Page 160  163 All Qs 1 st column only