Basic Concept of Ratios

Definition: Ratios are used to compare values. In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second. The ratio of two like quantities a and b is the fraction a/b, which indicates how many times b is the quantity a. In other words, their ratio indicates their relative sizes.

Example: Suppose three men receive their share of profit as 4000, 3000 and 1000. Find the ratio between their profits.

Solution:

The ratio of their share (profits) is

4000 : 3000 : 1000

= 4 : 3 : 1         (divided by 1000)

If x and y are two quantities of the same kind and with the same units such that y ≠ 0; then the quotient 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, Weight of the First person / Weight of the Second person = 40 kg / 80 kg = ½

We say, the ratio of the weight of the first person to the weight of the second person is ½ 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 6ft / 5ft, i.e., 6565 or 6 : 5. Here, 6 is the antecedent and 5 is the consequent.

Notice that, in the expression “the ratio of men to women”, “men” came first. This order is very important, and must be respected: whichever word came first, its number must come first. If the expression had been “the ratio of women to men”, then the numbers would have been “20 to 15”.

Expressing the ratio of men to women as “15 to 20” is expressing the ratio in words. There are two other notations for this “15 to 20” ratio:

• odds notation: 15 : 20
• fractional notation: 15/20

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