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

2/2

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

Addition of Fractions having the Same Denominator

Subtraction of Fractions having the Same Denominator

Addition and Subtraction of Fractions on the Fraction Number Line







4th Grade Math Activities

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