Definition: The ratio of two quantities of the same kind in the same units is the fraction that one quantity is of the other. Thus the ratio 'a is to b' is the fraction written as a : b, here b ≠ 0. In the ratio "a : b", 'a' is called as the 'first term' or 'antecedent' and 'b' is called as the second term or 'consequent'.
Examples on ratio definitions:
- The ratio between Rs.50 and Rs.10 is 50 : 10 = 50/10 = 5/1 = 5 : 1
- The ratio between 5 kg and 15 kg is 5 : 15 = 5/15 = 1/3 = 1 : 3
- The ratio between Rs.1 and 5 kg is not possible, since they are of different units.
Important property: The value of a ratio remains unchanged, if both of its terms are multiplied or divided by the same non-zero quantity.
Examples on important property:
5/15 = (5 * 8)/(15 * 8) shows that 5 : 15 is equal to 40 : 120
3/7 = [3/5]/[7/5] shows that 3 : 7 is equal to 3/5 : 7/5.
Ratio in simplest form: A ratio is said to be in simplest form, if antecedent (first term) and consequent (second term) have no common factors other than one. [It means their HCF is "1"].
Refer to adjacent image for an example.
Compound ratio: If a/b, c/d are two ratios then the compound ratio of a/b and c/d is a/b : c/d = ac/bd = ac : bd. In other words, compound ratio is the ratio of the product of antecedents to the product of consequents of the given ratios.
Example on compound ratio:
If P : Q = 8 : 6 and Q : R = 6 : 5 then P : Q : R = 8 : 6 : 5.
Another example is given at the adjacent.
Ratios of equality
A ratio x : y = x/y is called a ratio of greater inequality, if x is greater than the y.
A ratio x : y = x/y is called a ratio of less inequality, if x is less than the y.
A ratio x : y = x/y is called a ratio of equality, if x is equal to y.
A ratio of greater inequality (x > y) is reduced (to a lower ratio) by adding the same quantity to both its terms.
If the same quantity is subtracted from both the terms, the ratio of greater inequality is increased.
i.e, x/y > (x + a)/(y + a) and x/y < (x – a)/(y – a)
The converse is true for a ratio of less inequality (x < y).
i.e, x/y < (x + a)/(y + a) and x/y > (x – a)/(y – a)