# Conversion of a Fraction into its Smallest and Simplest Form

In conversion of a fraction into its smallest and simplest form are discussed here.

If the numerator and denominator of a fraction have no common factors then the fraction is considered as its smallest and simplest form, as 3/5, 2/3, 4/7, 7/11, etc., are the simplest forms of 6/10, 8/12, 20/35, 21/33 respectively.

Examples on conversion of a fraction into its smallest and simplest form:

1. Change 45/60 to its simplest form.

Solution:

45/60 = 3 x 3 x 5/3 x 2 x 2 x 5

All the factors of numerator and denominator are written;

45 = 3 x 3 x 5 and 60 = 3 x 2 x 2 x 5 (common factors are removed)

= 3/4

Thus, to get the simplest form of a fraction, the common factors of numerator and denominator are removed.

2. Change 15/75 to its simplest form.

Solution:

15/75 = 3 x 5/3 x 5 x 5

All the factors of numerator and denominator are written

15 = 3 x 5 and 75 = 3 x 5 x 5 (common factors are removed)

= 1/5

Thus, to get the simplest form of a fraction, the common factors of numerator and denominator are removed.

Reducing Fraction to the Lowest Term:

You have learnt to find equivalent fractions by multiplying and diving. Now let us try to reduce fractions to the lowest term.

 1. Fraction 9/12 ÷
 Common factor 3/3 = 3/4

Equivalent fraction in the lowest term.

2. Sometimes we need to divide more than once.

 16/248/124/6 ÷÷÷
 2/22/22/2 = 8/12= 4/6= 2/3

So, 16/24 = 2/3

Therefore, 2/3 is the lowest term

 3. Fraction 12/24 ÷
 H.C.F12/12 Lowest Term= 1/2

We have divided by the highest common factor

Note:

When the numerator and the denominator of the fraction cannot be divided by a factor greater than 1, the fraction is in its lowest term.

For example, 3/4, 2/3, 1/2

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