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# Ratios and Proportions

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A Ratio is nothing but two quantities compared with each other. The quantities to be compared should be of same unit. Since two similar quantities are compared in a ratio it does not have any unit. The ratio is written with : symbol. The ratios can also be represented as a fraction. The ratio of two quantities are written as, a:b. It can also be written as $\frac{a}{b}$.

When two ratios are equal they are called Proportions. The proportion is written as a : b = c : d. They are also written as $\frac{a}{b}$ $\frac{c}{d}$. The cross product of the two ratios can also be equalized a * d = b * c. If three values in a proportion are known then we can easily find the fourth value. For the proportion to be used, the ratios must be equal.

Some examples on how to represent ratios are given below:
1. The ratio of 4 and 9 is 4:9 ⇒ $\frac{4}{9}$
2. The ratio of 3 and 8 is 3:8 ⇒ $\frac{3}{8}$
3. The ratio of 50 and 150 is 50:150 ⇒ $\frac{50}{150}$ $\frac{1}{3}$
4. The ratio of 9 and 3 is 9:3 ⇒ $\frac{9}{3}$ ⇒ 3

Some examples on proportions are given below:

Example 1:

4:3 = x:9
$\frac{4}{3}$ = $\frac{x}{9}$
⇒ 4 * 9 = x * 3
⇒ x * 3 = 4 * 9
⇒ x = $\frac{4*9}{3}$
⇒ x = 12

Example 2:

12:4 = x:5
$\frac{12}{4}$ = $\frac{x}{5}$
⇒ 12 * 5 = x * 4
⇒ x * 4 = 12 * 5
⇒ x = $\frac{12*5}{4}$
⇒ x = 15