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

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

Did you find an error?

4. Ratio in simplest form