Simplify Fractions

Simplifying Fractions: Fractions are the essential part of arithmetic. A fraction is defined as a type of number which is represented in the form of pq, where q ≠ 0; where, p – the number above the bar is known as numerator and q – the number below the bar is termed as denominator.

How to Simplify Fractions

Fractions are to be simplified till there is no common factor in numerator and denominator. This process is called simplifying a fraction or reducing a fraction.

Simplifying a fraction does not always result in a simplest reduction of the fraction; since in some cases, higher equivalent fraction is required as the answer. Simplification could also result in an improper fraction. In such cases, we are needed to convert it in the form of a mixed fraction. Simplification could also end up in reducing the fraction to its lowest possible equivalent.

A fraction may be proper or improper fraction. Example: 48 is simplified as 12.

The process of simplifying fractions can be illustrated below:

Example 1: Simplify the fraction 120/54:

It has a common factor 2. So dividing by 2, we get 60/27. Still there is a common factor 3. After dividing by 3, we get simplified fraction 20/9.

he other way to understand this concept is given below.

Example 2: Simplify 96/184.

This fraction has common factor 2. Divide numerator and denominator by 2 until obtain simplified form. In this way, we get 12/23.

Simplifying Fractions with Variables

At times some fractions have terms with variables such 3x or 4xy. These fractions can be simplified easily if both numerator and denominator have same variable. Below are example for simplify fractions with variables.

here, we are going to learn about method of simplification of variables.

Question: Simplify fraction: $$\frac{x^3+x^2}{x^4-x^2}$$

$$\frac{x^3+x^2}{x^4-x^2}$$ = $$\frac{x^2(x+1)}{x^2(x^2-1^2)}$$
= $$\frac{x+1}{(x+1)(x-1)}$$
= $$\frac{1}{x-1}$$

Simplifying Fractions Examples

Question 1: Simplify: $$\frac{12}{144}$$

Solution:

First start with small number 2 which divides both 12 and 144.

$$\frac{12}{144}$$ $$\div$$ $$\frac{2}{2}$$ = $$\frac{12}{144}$$ $$\times$$ $$\frac{2}{2}$$ = $$\frac{6}{72}$$

$$\frac{6}{72}$$ $$\times$$ $$\frac{2}{2}$$ = $$\frac{3}{36}$$

$$\frac{3}{36}$$ $$\times$$ $$\frac{3}{3}$$ = $$\frac{1}{ 12}$$

The simplest form of given fraction is $$\frac{1}{12}$$.

Question 2: Solve $$\frac{6}{14}$$

Solution:

Given fraction is $$\frac{6}{14}$$

$$\frac{6}{14} \times \frac{2}{2}$$ = $$\frac{3}{7}$$

Therefore $$\frac{6}{14}$$ = $$\frac{3}{7}$$

Question 3: Reduce $$\frac{55}{44}$$

Solution:

Factor each number:

55 = 11. 5

44 = 11. 4

Greatest common factor of 44 and 55 is 11.

$$\frac{55}{44}$$ x $$\frac{11}{11}$$ = $$\frac{5}{4}$$

Question 4: Write simplest form of $$\frac{78}{68}$$

Solution:

Multiply and divide fraction by 2

$$\frac{78}{68}$$ x $$\frac{2}{2}$$ = $$\frac{39}{34}$$

The simplest form of given fraction is $$\frac{39}{34}$$

Simplifying Fractions Practice Problems

Practice Problems

Question 1: Simplify $$\frac{114}{1000}$$

Question 2: Reduce $$\frac{2x^3-8x}{x-2}$$