Lesson 10, Topic 1
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# Ratio

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A ratio is a way of comparing two or more quantities. The ratio is a relationship between two numbers indicating how many times the first number contains the second for example, if a basket contains, 8 oranges and 5 mangoes the ratio of oranges to mangoes is 8 ratio 5, written as 8:5 or 8 to 5.

‘Ratio’ can be written in the following form.

1. m : n

2. m to n

3. $$\frac{m}{n}$$ (as fraction)

### Equivalent Ratio:

Equivalent Ratios are Equal Ratios

Example 1

a. 3 : 4,  6 : 8,   9 : 12,  12 : 16 are equivalent ratio because:

3 : 4

=  3 x 2 : 4 x 2 = 6 : 8

=  3 x 3 : 4 x 3 =  9 : 12

=  3 x 4 : 4 x 4   = 12 : 16

b. 100 : 50,  50 : 25,  20 : 10, 10 : 5 are equivalent because

100 : 50

=  (100 ÷ 2) : (50 ÷ 2)  =  50 : 25

= (100 ÷ 5): (50 ÷ 5) =  20 : 10

= (100 ÷ 10) : (50÷ 10) = 10 : 5

### Simplifying Ratio:

This is writing a ratio in its simplest form or smaller numbers. To simplify any given ratio, divide both its numerator and denominator by the same number until it can no longer be simplified.

Example 2

Express the following ratio in their simplest forms

a. 21 : 14

b. 6 : 15

c. 5 : 1$$\frac{1}{2}$$

d. 0.5 : 25

Find the factor that can cancel each number in the simplication process.

Solution

a. 21 : 14 = $$\frac{21}{14}\\ \scriptsize divide \: by \: 7\\ = \frac{3}{2} \\ = \scriptsize 3 : 2$$

b. 6 : 15 = $$\frac{6}{15}\\ \scriptsize divide \: by \: 3 \\ = \frac{2}{5} \\= \scriptsize 2:5$$

c. 5 : 1$$\frac{1}{2}$$ = $$\frac{5}{1\frac{1}{2}} \\ = \frac{5}{\frac{3}{2}} \\ = \frac{5}{1} \: \div \: \frac{3}{2}\\= \frac{5}{1} \: \times \: \frac{2}{3} \\ = \frac{10}{3}\\= \scriptsize 10 \: : \:3$$

d. 0.5 : 25 = $$\frac{5}{10} \scriptsize \: \div \: 25 \\ = \frac{5}{10} \: \times \: \frac{1}{25} \\ = \frac{5}{250} \\ = \frac{1}{50} \\ = \scriptsize 1\: : \: 50$$ error: