RATIO & PROPORTIONS

 RATIO & PROPORTION

Ratio 

A ratio is a comparison of two quantities.

● A ratio can be written as a fraction; ratios are mostly written in the simplest form.

● In the above example, the ratio of rice to water in terms of the number of cups

can be written in three different ways as 1 : 2 or 1/2 or 1 to 2 .

Properties of Ratio

● A ratio has no unit. It is a number. For example, the ratio of 8 km to 4 km is written as 8 : 4 = 2 : 1 and not 2 km : 1 km.

● The two quantities of a ratio should be of the same unit. The ratio of 4 km to 400 m is expressed as (4 × 1000) : 400 = 4000 : 400 = 10 : 1

● Each number of the ratio is called a term.

● Order of the terms in a ratio cannot be reversed. 

We can get equivalent ratios by multiplying or dividing the numerator and denominator by

a common number.

Proportion

When two ratios are equal , we say that the ratios are in Proportion. This is

denoted as a : b : : c : d and it is read as ‘a is to b as c is to d’. 

Proportionality law

If two ratios are in proportion ie., a : b : : c : d then the product of the extremes is equal to the product of the means. This is called the proportionality law. Here, a and d are the extremes and b and c are the means. Also, if two ratios are equal ie., is called the cross product of proportions.