Concept of proportion — lesson. Mathematics State Board, Class 6.

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Sahas bought \(6\) chocolates for \(₹30\), and Sree bought \(11\) chocolates for \(₹55\).

Can you guess whose chocolate is more expensive?

Let us use the ratio concept to compare the cost.

The ratio of the number of chocolates to its cost bought by Sahas \(=\) \(6:30\).

It's the simplest form when dividing by \(6\) becomes

\frac{6 \div 6}{30 \div 6} = \frac{1}{5} = 1 : 5

The ratio of the number of chocolates to its cost bought by Sree \(=\) \(11:55\).

It's the simplest form when dividing by \(6\) becomes

\frac{11 \div 11}{55 \div 11} = \frac{1}{5} = 1 : 5

Note that both ratios are equal.

Both Sahas and Sree bought chocolates for the same prize.

If two ratios \(a:b\) and \(c:d\) are equal, then we say that they are in proportion. Use the symbol '\(::\)' or '\(=\)' to denote the proportion.

Example:

Check whether the given ratios are equal/proportion.

1. \(2:4\) and \(8:16\).

Reducing the first ratio to the simplest form becomes as follows:

\frac{2}{4} = \frac{2 \div 2}{4 \div 2} = \frac{1}{2} = 1 : 2

Reducing the first ratio to the simplest form becomes as follows:

\frac{8}{16} = \frac{8 \div 8}{16 \div 8} = \frac{1}{2} = 1 : 2

Here the simplest form of the given ratios is equal. Thus, the two ratios are in proportion.

2. \(9:4\) and \(18:6\).

The first ratio \(9:4\) is already in simplest form. So let us reduce the second ratio.

\frac{18}{6} = \frac{18 \div 6}{6 \div 6} = \frac{3}{1} = 3 : 1

Note that the simplest form of the given ratios is not equal. Thus, the two ratios are not in proportion.

Did you find an error?

1. Concept of proportion