# Simplify Fraction || Reducing Fraction in lowest terms

In this post we will learn how to reduce fraction to its lowest terms. After that we will see some examples and solved problems related to this topic.

## What does fraction simplification means?

In fractions, usually there is some common factors in both numerator and denominator.

With simplification we reduce the fractions to its lowest order such that there is no common factor left between numerator and denominator.

## Why we do fraction simplification?

We know that numbers are used in various context.
Whether it is Physics or Accounting, we use numbers to measure different parameters.

Arranging numbers in simple manners help us gain better insight about the data presented. Hence, we should know how to present numbers in as simple way as possible.

## How to simplify fraction?

Here we will learn two methods for fraction simplification:

(A) Simplification using HCF
(B) Simplification using direct division

### Fraction Simplification using HCF

In order to simplify fraction, follow the below steps:

(a) Write all the factors of numerator by finding H.C.F

(b) Now find all the denominator factors using H.C.F

(c) Eliminate the common factors between the numerator and denoinator

(d) Multiply all the remaining factors and you will have your simplified fraction.

The steps are easy and need basic understanding of HCF.

Let us look at some of the examples to understand the above method.

Example 01
Simplify the fraction \mathtt{\frac{4}{6}}

(a) Find factors of numerator using HCF

HCF of number 4 is given below:

Factors of 4 ⟹ 2 x 2

(b) Find factors of denominator using HCF

HCF of number 6 is given below:

Factors of 6 ⟹ 2 x 3

(c) Eliminate the common factors of numerator and denominator

Remember that factors are form of division, hence you can cancel out the common numbers present in numerator and denominator.

The fraction is expressed as:

\mathtt{\Longrightarrow \ \ \frac{4}{6}}\\\ \\ \mathtt{\Longrightarrow \ \ \frac{2\times 2}{2\times 3}}

Cancel out 2 from numerator and denominator, we get;

\mathtt{\Longrightarrow \ \ \frac{2}{3}}

Hence, we have reduced the fraction 4/6 to its simplest form i.e. 2/3

Example 02
Simplify the fraction \mathtt{\frac{11}{66}}

(a) Find factors of numerator

Factor of 11 ⟹ 11

(b) Find factor of denominator

Factor of 66 ⟹ 2 x 3 x 11

(c) Eliminate the common factors between numerator and denominator.

The fraction is expressed as:

\mathtt{\Longrightarrow \ \ \frac{11}{66}}\\\ \\ \mathtt{\Longrightarrow \ \ \frac{11}{2\times 3\times 11}}

Cancel out 11 from numerator and denominator, we get;

\mathtt{\Longrightarrow \ \ \frac{1}{2\times 3}}\\\ \\ \mathtt{\Longrightarrow \ \ \frac{1}{6} \ }

Hence the fraction 11/66 is simplified to 1/6

Example 03
Simplify the fraction \mathtt{\frac{7}{50}}

(a) Find the factors of numerator

Factors of 7 ⟹ 7

(b) Now find factors of denominator

Factors of 50 ⟹ 2 x 5 x 5

(c) Remove the common factors between numerator and denominator

The fraction is expressed as:

\mathtt{\Longrightarrow \ \ \frac{7}{50}}\\\ \\ \mathtt{\Longrightarrow \ \ \frac{7}{2\times 5\times 5}}

Note that there is no common factors between the numerator & denominator.

Hence, the fraction 7/50 cannot be simplified further.

Example 04
Simplify the fraction \mathtt{\frac{12}{42}}

(a) Find all the factors of numerator

Factors of 12 ⟹ 2 x 2 x 3

(b) Find factors of denominator

Factors of 42 ⟹ 2 x 3 x 7

(c) Remove the common factors between numerator and denominator

The fraction is expressed as:

Hence, the fraction 12/42 is simplified to 2/7

### Simplification of fraction using direct division

In this method we divide both the numerator and denominator by prime numbers like 2, 3, 5, 7, 11 . . . etc. until no further division is possible.

This is fast and direct technique of fraction simplification which requires good division technique among the students.

Example 01
Simplify the fraction \mathtt{\frac{12}{30}}

Both the numbers are divisible by 2.
So divide numerator and denominator by 2

After dividing by 2 we get fraction (6/15)

In fraction (6/15), both numerator and denominator is divisible by 3.
Dividing numerator and denominator by 3

Here we get fraction (2/5).

The fraction (2/5) is not divisible by any number.
Hence, the fraction 12/30 is simplified to 2/5

Example 02
Simplify the fraction \mathtt{\frac{52}{16}}

Divide numerator & denominator by 2

We got the fraction 26/8.
Again both the numerator and denominator is divisible by 2.

We got the fraction (13/4).
There is no common factor left between numerator and denominator, hence 13/4 is the simplest fraction.

Note: The direct property is useful for someone with good calculation skills. If you are facing any difficulty, ignore this method and practice the above mentioned H.C.F method.

## Problems on reducing Fractions in lowest terms

(01) Simplify the fraction \mathtt{\frac{8}{28}}

Factors of numerator
8 = 2 x 2 x 2

Factors of denominator
28 = 2 x 2 x 7

The fraction can be represented as:
\mathtt{\Longrightarrow \ \ \frac{8}{28} \ }\\\ \\ \mathtt{\Longrightarrow \ \ \frac{2\times 2\times 2}{2\times 2\times 7}}

Removing the common factors in numerator and denominator, we get;

\mathtt{\Longrightarrow \ \ \frac{2}{7}}

Hence, we reduced the fraction (8/28) to (2/7)

(02) Simplify the fraction \mathtt{\frac{14}{35}}

Factors of numerator
14 = 2 x 7

Factors of denominator
35 = 5 x 7

Remove the common factors of numerator and denominator.
The fraction is represented as:

Hence, 2/5 is the simplified fraction

(03) Simplify the fraction \mathtt{\frac{25}{50}}

Factors of numerator
25 = 5 x 5

Factors of denominator
50 = 2 x 5 x 5

Remove the common factors from numerator and denominator.
The fraction is expressed as:

Hence, 1/2 is the simplified fraction.

(04) Simplify the fraction \mathtt{\frac{16}{13}}

Factors of numerator
16 = 2 x 2 x 2 x 2

Factors of denominator
13 = 13

Note that there is no common factor between numerator and denominator.
Hence, fraction 16/13 cannot be further simplified.

(05) Simplify the fraction \mathtt{\frac{100}{30}}