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: 4 x 2 =  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$$\frac{1}{2}$$ = $$\frac{5}{1\frac{1}{2}} \\ = \frac{5}{\normalsize \frac{3}{2}} \\ = \frac{5}{1} \: \div \: \frac{3}{2}\\= \frac{5}{1} \: \times \: \frac{2}{3} \\ = \frac{10}{3}\\= \scriptsize 10 \: : \:3$$

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

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