Ratio in simplest form — lesson. Mathematics State Board, Class 6.

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There are two cases in simplifying the ratio.

Simplifying ratios of the same unit.
Simplifying ratios of the different unit.

Simplifying ratios of the same unit

The general rule to simplify the ratios of the same unit.

Step

$1$ : Write the ratio in fraction form.

Step

$2$ : Divide each of the ratios with a suitable number.

Example:

1. Simplify the ratio

$45$ to

$6$ .

The fraction form of the ratio is

$\frac{45}{6}$ .

Divide each of the ratios by

$3$ .

That is

$\frac{45 \div 3}{6 \div 3} = \frac{15}{2} = 15 : 2$ .

Thus, the simplified form of the ratio is

$15 : 2$ .

2. Simplify the ratio of

$750$

$gm$ to

$25$

$gm$ .

The fraction form of the ratio is

$\frac{750}{25}$ .

Divide each of the ratios by

$25$ .

That is

$\frac{750 \div 25}{25 \div 25} = \frac{30}{1} = 30 : 1$ .

Thus, the simplified form of the ratio is

$30 : 1$ .

Simplifying ratios of different units.

The general rule to simplify the ratios of the different unit.

Step

$1$ : Convert the ratios to the same unit.

Step

$2$ : Write the ratio in fraction form.

Step

$3$ : Divide each of the ratios with a suitable number.

Example:

Simplify the ratio

$5$

$m$ to

$700$

$cm$ .

Step

$1$ : Convert

$5$

$m$ to

$cm$ . We know that

$1m = 100cm$ . Thus,

$5m = 5 × 100 = 500cm$ .

Step

$2$ : Write the ratio in fraction form. The fraction form of the given ratios is

$\frac{500}{700}$ .

Step

$3$ : Divide each number by

$100$ .

$\frac{500}{700} = \frac{5}{7} = 5 : 7$ .

Thus, the simplified form of the ratio is

$5 : 7$ .

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4. Ratio in simplest form

Theory: