# Simplifying Ratios

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Ratio is the quantitative comparison between quantitates or numbers. Ratio is a very commonly used operation in mathematics. Ratio helps in solving questions related to comparisons, proportions and many more. The symbol of ratio is “:”.  For example, a / b can be written as a : b. Here a / b is fraction form and a:b is the ratio form. The simplification of ratio is writing the given ratio in the most simplified from possible.

Example 1: Are the ratio’s equivalent?
25 students taking Science class and 75 students taking English class.
15 students taking Science class and 45 students taking English class.

Solution: Here for the given question the ratio is between the number of students taking Science class and the number of students taking English class.

The first ratio given is, number of students Science : English = 25 : 75.

Simplifying the ratio gives 1 : 3.

The second ratio given is, number of students Science : English = 15 : 45

Simplifying the ratio gives 1 : 3.

Therefore the two ratios are equivalent.

Example 2: Simplify the given ratio 28 : 56

Solution: Here the given ratio is 48 : 96.

The fraction form can be written as 48/96.

The number 48 can be written as; 28 = 2 * 2 *7.

The number 56 can be written as 56 = 2 * 2 * 2 * 7.

Canceling the common factors simplifies the fraction to 1/2.

Hence the simplified ratio is 1 : 2.