Ratio and Proportion

Ratio is used for comparing two quantities of the same kind. The ratio formula for two numbers, a and b is expressed as a : b or a/b. When two or more ratios are equal, they are said to be in proportion. The concept of ratio and proportion is based on fractions.

What is Ratio and Proportion?

A comparison of two quantities by division is called a ratio and the equality of two ratios is called proportion. A ratio can be written in different forms like x : y or x/y and is commonly read as, x is to y.

On the other hand, proportion is an equation that says that two ratios are equivalent. A proportion is written as x : y : : z : w, and is read as x is to y as z is to w. Here, x/y = z/w where w & y are not equal to 0.

Definition of Proportion

Proportion refers to the equality of two ratios. Two equivalent ratios are always in proportion. Proportions are denoted by the symbol (: :) and they help us to solve for unknown quantities. In other words, proportion is an equation or statement that is used to depict that the two ratios or fractions are equivalent.

There are two types of proportions.

l Direct Proportion

l Inverse Proportion

Direct Proportion

Direct proportion describes the direct relationship between two quantities. If one quantity increases, the other quantity also increases and vice-versa. Thus, a direct proportion is written as y ∝ x. For example, if the speed of a car is increased, then it covers more distance in a fixed period of time.

Inverse Proportion

Inverse proportion describes the relationship between two quantities in which if one quantity increases, the other quantity decreases and vice-versa. Thus, an inverse proportion is written as y ∝ 1/x. For example, as the speed of a vehicle is increased, it will cover a fixed distance in less time.

Important Notes on Ratio and Proportion

1. Any two quantities with the same units can be compared.

2. Two ratios are said to be in proportion only if they are equal.

3. To check whether two ratios are equal and are in proportion, we can also use the cross-product method.

4. If we multiply and divide each term of a ratio by the same number, the ratio remains the same.

5. For any three quantities, if the ratio between the first and the second is equal to the ratio between the second and the third, then these are said to be in a continued proportion.

6. Similarly, in the case of any four quantities in a continued proportion, the ratio between the first and the second is equal to the ratio between the third and the fourth