We will discuss here about the basic concept of ratios.
Definition: The ratio of two like quantities a and b is the fraction \(\frac{a}{b}\), which indicates how many times b is the quantity a. In other words, their ratio indicates their relative sizes.
If x and y are two quantities of the same kind and with the same units such that y ≠ 0; then the quotient \(\frac{x}{y}\) is called the ratio between x and y.
Let the weights of two persons be 40 kg and 80 kg. Clearly, the weight of the second person is double the weight of the first person because 80 kg = 2 × 40 kg.
Therefore, \(\frac{Weight of the first person}{Weight of the second person}\) = \(\frac{40 kg}{80 kg}\) = \(\frac{1}{2}\).
We say, the ratio of the weight of the first person to the weight of the second person is \(\frac{1}{2}\) or 1 : 2.
The ratio of two like quantities a and b is the quotient a ÷ b, and it is written as a : b (read a is to b).
In the ratio a : b, a and b are called terms of the ratio, a is called the antecedent or first term, and b is called the consequent or second term. Then, ratio of two quantities = antecedent : consequent.
Example: The ratio of heights of two persons A and B whose heights are 6 ft and 5 ft is \(\frac{6 ft}{5 ft}\), i.e., \(\frac{6}{5}\) or 6 : 5. Here, 6 is the antecedent and 5 is the consequent.
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