** Fraction vs Ratio **

There are several ways of comparing the sizes of similar quantities, out of those, fraction and ratio are the two most popular.

Let us consider the following example:

A bar of chocolates was divided into 12 pieces. Tom ate 4 pieces and David ate the remaining 8 pieces.

We can compare the number of pieces of chocolate that they ate in various ways.

*(i). The difference between the pieces of chocolate they ate is 8 – 4 = 4.*

*Therefore, Tom ate 4 pieces less than David did.*

*(ii). (The number of pieces of chocolate that Tom ate)/(The number of pieces of chocolate that David ate)=4/8=1/2*

*i.e., Tom ate half the number of pieces that David did.*

**Ratio**

A comparison such as (ii) of the above example is known as a comparison by division. When two similar quantities are compared by division, a ratio is formed. For the above example, we say that the ratio of the number of pieces of chocolate that Tom ate to the number of pieces of chocolate that David ate is 4 to 8.

A ratio between two quantities is a number that expresses the numerical relationship between the two or more quantities relative to each other. The ratio of a to b (b ≠ 0) is denoted by a/b or as a to b or a:b. a is the ‘first term’ and is known as the antecedent and ‘b’ is the second term or consequent.

In the above example, the ratio is 4:8. That can also be written as 1:2, since 4/8=1/2= 1:2 expresses the ratio in the lowest terms or in the simplest form.

Since a/b=ma/mb for any natural number m, the ratio a:b equals the ratio ma:mb. Therefore, the value of a ratio remains the same if the antecedent and the consequent are multiplied or divided by the same quantity.

We can also compare more than two quantities. For an example, the ratio between three quantities can be expressed as a:b:c.

**Fraction**

A fraction is an example of a type of ratios. A fraction can be defined as a “part – whole” relationship of a quantity rather than as a comparative relationship between two separate quantities. When we use a fraction to represent a ratio between two, it is only a symbol. It is not equals to the value get by division.

For an example, the ratio 1:2 we can also express as 1/2. The value of this division is equals to 0.5. However, if we are using a fraction as a representation of ratio, we cannot say that the ratio 1/2 is equals to 0.5, as the whole is divided into three parts.

• Ratio is a relationship between two or more quantities. • Fraction is a type of ratio. |