To know about the properties of ratios it’s important to know that a ratio is a method to compare two quantities of the same kind with same unit; by dividing first quantity by the second. It is denoted by the colon ':'.
The ratio of P to Q = P/Q, and it is represented as P : Q. The quantities P and Q are called terms; P is the antecedent and Q is the consequent.
Suppose there are two mobile towers of heights 25 m and 15 m. Now to compare their heights we divide the height of the first mobile tower by the height of the second mobile tower and get (25 m)/(15 m) = (25 ÷ 5)/(15 ÷ 5) [dividing both numerator and denominator by 5] = 3/2.
Thus, it is evident from the above discussion that the height of the first mobile tower is 3/2 times the height of the second mobile tower and the fraction 3/2 is called the ratio of the heights of the two mobile towers. Therefore, we can also say that the ratio of heights of the mobile towers is 3 : 2.
Properties of Ratios:
1. The ratio of a number ‘P’ to the another number ‘Q’ (Q ≠ 0) is a fraction P/Q, and it is written as P : Q.
2. In the ratio P : Q, the first term is P and second term is Q.
3. In the ratio P : Q, the first term P is called antecedent and the second term Q is called consequent.
4. The two quantities compared in a ratio must have the same units of measurement.
In order to find the ratio between two quantities, both the quantities must be in the same unit e.g., ratio between 30 cm and 2 metre
= 30 cm : 200 cm [Since, 2 metre = 200 cm]
= 3 : 20
5. The ratio of two numbers is always expressed in its lowest terms in simplest form.
6. When two ratio P : Q is in its lowest term, P and Q are co-prime, or their HCF is 1.
7. The ratio of two quantities is an abstract quantity, i.e., it has no units in itself.
8. A ratio is a pure number.
9. The order of a ratio is important. By reversing the antecedent and the consequent of a ratio, a different ratio is obtained.
10. The ratio can be expressed as a fraction and a decimal.
11. The antecedent and the consequent of a ratio are always expressed as whole numbers. When they are not, they are converted into whole numbers.`