Concept of Ratio

In concept of ratio we will learn how a ratio is compared with two or more quantities of the same kind. It can be represented as a fraction.

A ratio is a comparison of two or more quantities of the same kind. It can be represented as a fraction.

Most of time, we compare things, number, etc. (say, m and n) by saying:

(i) m greater than n

(ii) m less than n

When we want to see how much more (m greater than n) or less (m less than n) one quantities is than the other, we find the difference of their magnitudes and such a comparison is known as the comparison by division.

(iii) m is double of n

(iv) m is one-fourth of n

If we want to see how many times more (m is double of n) or less (m is one-fourth of n) one quantities is than the other, we find the ratio or division of their magnitudes and such a comparison is known as the comparison by difference.

(v) \(\frac{m}{n}\) = \(\frac{2}{3}\)

(vi) \(\frac{n}{m}\) = \(\frac{5}{7}\), etc.

The method of comparing two quantities (numbers, things, etc.) by dividing one quantity by the other is called a ratio.

Thus:  (v) \(\frac{m}{n}\) = \(\frac{2}{3}\) represents the ratio between m and n.

         (vi) \(\frac{n}{m}\) = \(\frac{5}{7}\) represents the ratio between n and m.

When we compare two quantities of the same kind of division, we say that we form a ratio of the two quantities.

Therefore, it is evident from the basic concept of ratio is that a ratio is a fraction that shows how many times a quantity is of another quantity of the same kind.

Definition of Ratio:

The relation between two quantities (both of them are same kind and in the same unit) obtain on dividing one quantity by the other, is called the ratio.

The symbol used for this purpose " : " and is put between the two quantities compared.

Therefore, the ratio between two quantities m and n (n ≠ 0), both of them same kind and in the same unit, is \(\frac{m}{n}\) and often written as m : n (read as m to n or m is to n)

In the ratio m : n, the quantities (numbers) m and n are called the terms of the ratio. The first term (i.e. m) is called antecedent and the second term (i.e. is n) is called consequent.

Note: From the concept of ratio and its definition we come to know that when numerator and denominator of a fraction are divided or multiplied by the same non-zero numbers, the value of the fraction does not change. In this reason, the value of a ratio does not alter, if its antecedent and consequent are divided or multiplied by the same non-zero numbers.

For example, the ratio of 15 and 25 = 15 : 25 = \(\frac{15}{25}\)

Now, multiply numerator (antecedent) and denominator (consequent) by 5

\(\frac{15}{25}\) = \(\frac{15 × 5}{25 × 5}\) = \(\frac{75}{125}\)

Therefore, \(\frac{15}{25}\) = \(\frac{75}{125}\)

Again, divide numerator (antecedent) and denominator (consequent) by 5

\(\frac{15}{25}\) = \(\frac{15 ÷ 5}{25 ÷ 5}\) = \(\frac{3}{5}\)

Therefore, \(\frac{15}{25}\) = \(\frac{3}{5}\)

Examples on ratio:

(i) The ratio of $ 2 to $ 3 = \(\frac{$ 2}{$ 3}\) = \(\frac{2}{3}\) = 2 : 3.

(ii) The ratio of 7 metres to 4 metres = \(\frac{\textrm{7 metres}}{\textrm{4 metres}}\) = \(\frac{7}{4}\) = 7 : 4.

(iii) The ratio of 9 kg to 17 kg = \(\frac{\textrm{9 kg}}{\textrm{17 kg}}\) = \(\frac{9}{17}\) = 9 : 17.

(iv) The ratio of 13 litres to 5 litres = \(\frac{\textrm{13 litres}}{\textrm{5 litres}}\) = \(\frac{13}{5}\) = 13 : 5.

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