# Simplest Form

In mathematics, when we divide a complete part into some equal parts then each part shows the fraction of whole part. Like pizza, pizza is a circular in shape, if we divide it in 8 equal parts then each part is the fraction of whole part.

Fractions are written in the form of ratio of two numbers. The upper number is called as numerator and the number below is called as denominator.

For example: a/b is the fraction, in which a is numerator and b is the denominator. ## Simplest form:

Thus, fraction is the part of the whole number written in the form of numerator and denominator..

When numerator is expressed in its factors form and denominator is also written in factors form, then the common factors will be cancelled from numerator and denominator. Thus, finally we got the fraction which has its simplest form and can never further be simplified. Such type of form is called as simplest form.

By understanding the following examples we shall clear the concept of simplest form.

#### For example:

• 5/15 is the proper fraction as numerator is less than the denominator, and we convert it into simplest form as follows.

The factors of 5 are 1 and 5 only as it is the prime number. And the factors of 15 are 1, 3, and 5.

Hence 5 = 1*5 and 15 = 1*3*5

Thus,

5/15 = 5*1/ 1*3*5 = 1/3

Thus, 1/3 is the simplest form of proper fraction 5/15.

• Also, we can convert the 15/12 which is the improper fraction as numerator is greater than the denominator into the simplest form as follows.

12 can be written as 12= 1*3*4 and 15 = 1*3*5

Thus, 15/12 = 1*3*5/ 1*3*4 = 5/4

Thus we got the simplified form as 5/4 of the improper fraction 15/12.

• Also, we can convert the proper fraction 8/10 into the simplest form as follows.

8 can be written as 8 = 1*2*4 and 10 = 1*2*5

Thus, 8/10 = 1*2*4/ 1*2*5 = 4/5

And 4/5 cannot be further simplified as there is no common factor between 4 and 5.

Thus, 4/5 is the simplest form of proper fraction 8/10.

In this way, we can convert the proper fractions, improper fractions into the simplest form which is also its equivalent fraction form. And the simplest form cannot be further simplified into any other fraction.

Updated: July 14, 2021 — 11:16 pm