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.

$Reducing Fraction$

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.

16/24

8/12

4/6

2/2

= 8/12

= 4/6

= 2/3

So, 16/24 = 2/3

Therefore, 2/3 is the lowest term

3. Fraction

12/24

H.C.F

12/12

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

Related Concept

● Fraction of a Whole Numbers

● Representation of a Fraction

● Equivalent Fractions

● Properties of Equivalent Fractions

● Like and Unlike Fractions

● Comparison of Like Fractions

● Comparison of Fractions having the same Numerator

● Types of Fractions

● Changing Fractions

● Conversion of Fractions into Fractions having Same Denominator

● Conversion of a Fraction into its Smallest and Simplest Form