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# How to do Ratios?

A ratio expresses the relationship between two quantities which are usually of the same kind such as vegetables, fruits, objects, fluids, people etc. Ratios show the comparison between two objects. It represents quantity (not necessarily whole number) of a particular attribute as compared to other.

For example: Ratio of flour and sugar in a recipe is 3 to 1 means that quantity of flour should be 3 times the quantity of sugar.

Ratios Notation:

Ratios are denoted in many ways as follows:

• a : b
• a to b
• a is to b
• a / b
• $\frac{a}{b}$

For example, if there are 5 parrots and 3 peacocks in a zoo, then their ratio can be expressed as 5 : 3 or 5 to 3 or 5 is to 3 or 5 / 3 or $\frac{5}{3}$.

Ratios basically can be categorized in to two ways:

• Part to Part: Comparison between one part and another.
• Part to Whole (Whole to Part): Comparison between one part and total quantity.

Look at the jar full of colorful balls shown below:

There are 3 red, 4 blue, 2 green, and 5 black balls in it. Part to part ratios may be referred as ratio of red to blue balls (3 : 4), ratio of black to green balls (5 : 2) etc. Part to whole ratios may be the ratio of blue to total balls (4 : 14 or 2 : 7), black to total balls (5 : 14) etc.

Let us take an example related to ratios.

Example:

Ratio of number of boys and girls present on a particular day in a class is  5 : 6. If 20 boys were present, calculate the total number of girls present that day.

Solution:

Ratio of boys to girls = 5 : 6

$\frac{\text{Number of boys}}{\text{Number of girls}}$ = $\frac{5}{6}$

$\frac{20}{\text{Number of girls}}$ = $\frac{5}{6}$

Cross multiplying the expression, we get

Number of girls = $\frac{20 \times 6}{5}$

Number of girls = 24

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