### Ratio and proportions

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__Ratio and Proportion__

Ratio

A ratio is a relationship between two numbers by division of the same kind. The Ratio of a to b is written as

a : b =

b

a

In ratio a : b, we can say that a as the first term or antecedent and b the second term or consequent.

**Rule of Ratio :**In ratio multiplication or division of each an every term of a ratio by the same non- zero number does not affect the ratio.Proportion

The idea of proportions is that two ratios are like equal.

If a : b = c : d, we write a : b : : c : d,

Ex. 3 / 15 = 1 / 5

a and d called extremes, where as b and c called mean terms.

If a : b = c : d, we write a : b : : c : d,

Ex. 3 / 15 = 1 / 5

a and d called extremes, where as b and c called mean terms.

Proportion of quantities

The four quantities like a, b, c, d we can say proportion then we can express it

a : b = c : d

Then a : b : : c : d <-> ( a x d ) = ( b x c )

a : b = c : d

Then a : b : : c : d <-> ( a x d ) = ( b x c )

product of means = product of extremes.

If there is given three quantities like a, d, c of same like then we can say it proportion of continued.
a : d = d : c , d is called mean term. a and c are called extremes.