Simplifying Fractions
Simplifying a fraction means to reduce a fraction to its simplest form. A fraction is in its simplest form if its numerator and denominator have no common factors other than 1. The given fraction is equivalent to its simplest form. An important step that we do while we solve fraction problems is to reduce them to the simplest form. Though we simplify them, the value of the fraction is going to remain unchanged. This means the simplified fraction and the actual fraction form a pair of equivalent fractions. In this minilesson, we will learn a few easy ways to simplify fractions.
1.  How to Simplify Fractions? 
2.  Easy Ways to Simplify Fractions 
3.  Simplifying Mixed Fractions 
4.  Simplifying Improper Fractions 
5.  FAQs on Simplifying Fractions 
How to Simplify Fractions?
Simplifying a fraction implies reducing a fraction to its lowest form. A fraction is in its simplest form if its numerator and denominator have no common factors except 1. The simplest form of a fraction is equivalent to the given fraction. For example, the fraction 3/4 is in the simplest form because 3 and 4 have no common factor except 1.
Let's try simplifying the fraction 8/24 step by step.
Simplify Fractions Step by Step
Here is a step by step process for you to understand the process of simplifying a fraction. Consider the fraction, 8/24 and follow the steps mention below to understand how to simplify the fraction 8/24.
Step 1: Write the factors of numerator and denominator.
The factors of 8 and 24 are
 Factors of 8: 1, 2, 4, and 8
 Factors of 24: 1, 2, 3, 4, 6, 8, 12, and 24
Step 2: Determine the common factors of numerator and denominator. The common factors of 8 and 24 are 1, 2, 4, and 8
Step 3: Divide the numerator and denominator by the common factors until they have no common factor except 1. The fraction so obtained is in the simplest form. Let's start dividing by 2, then 8/24 = (8/2)/(24/2) = 4/12. We will continue to divide by 2 until we can't go any further. So, we have (4/2)/(12/2) = 2/6 = (2/2)/(6/2) = 1/3.
Thus, 1/3 is the simplest form of the fraction 8/24.
Easy Ways to Simplify Fractions
We can make a complicated fraction as simple as possible by following the process of simplifying the fraction. In order to find the simplified forms of fractions, take a look at a few easy ways to simplify the fraction. Here we have threesixths of a pizza.
Why say threesixths when you really mean half?
Simplifying a fraction means making a fraction as simple as possible. A quick way to find the simplest form of a fraction is to work out with the highest common factor. Follow the steps given below to learn the shortest way.
 Step 1: Write the factors of numerator and denominator.
 Step 2: Determine the highest common factor of numerator and denominator.
 Step 3: Divide the numerator and denominator by the highest common factor. The fraction so obtained is in the simplest form.
Let's get back to the same problem of simplifying the fraction 8/24. The highest common factor of 8 and 24 is 8. Dividing the numerator 8 and the denominator 24 by 8 will directly give us the simplest form of the fraction, that is, 1/3. So, the shortest way to break down a fraction into its simplest form is to divide the numerator and denominator by its highest common factor.
Simplifying Fraction with Variables
You can also simplify the fraction containing variables in the numerator and denominator. Use the expanded form of each term in the numerator and denominator to make it easy for you to simplify the fraction with variables.
Let's simply the fraction (x^{2}y)/(xy).
Express the numerator and denominator as the product of variables.
(x^{2}y)/(xy) =(x × x × y)/(x × y)
Cancel out the common variables.
(x^{2}y)/(xy) =(x × x × y)/(x × y) = x
We hope simplifying fractions with variables have been easy for you.
Simplifying Fractions with Exponents
You can simplify the fraction containing exponents in the numerator and denominator. Use the expanded form of exponents in the numerator and denominator to make it easy for you to simplify the fraction with exponents. To make a number easy to read, we sometimes make use of exponents.
Suppose we have the fraction 3^{5}/3^{2}
We will express the numerator and denominator as the product of numbers and then cancel out the common numbers.
3^{5}/3^{2} = (3 × 3 × 3 × 3 × 3)/(3 × 3) = 3 × 3 × 3 = 27
So, you finally learned the way of simplifying the fractions with exponents.
Simplifying Mixed Fractions
A mixed fraction is a mixture of a whole and a fraction. In order to simplify a mixed fraction, you need to simplify the fractional part only. For that write the numerator and the denominator in factored form and cancel out the common factors. The resultant will be the new numerator and the new denominator of the mixed fraction.
For example: Simplify the mixed fraction \(3\dfrac{4}{10}\).
To simplify the mixed fraction \(3\dfrac{4}{10}\), only simplify the fractional part. Write the numerator and denominator of the fractional part in factored form and cancel out the common factors.
4/10 = (2 × 2)/(2 × 5) = 2/5
Therefore, the mixed fraction \(3\dfrac{4}{10}\) can be simplified as \(3\dfrac{2}{5}\)
Simplifying Improper Fractions
Improper fractions are those in which the numerator is greater than the denominator and a mixed fraction is a mixture of a whole and a proper fraction. To simplify improper fractions we need to convert them to mixed fractions, for that we need to divide the numerator by the denominator. Then, we write it in the mixed number form by placing the quotient as the whole number, the remainder as the numerator, and the divisor as the denominator. Let us go through the following example to understand this better.
For example: To simplify the improper fraction 11/4, we need to divide 11 by 4 and get the values of quotient and remainder after performing division.
When we divide 11/4, we get 2 as the quotient and 3 as the remainder.
Therefore, the simplified form of the improper fraction 11/4 is \(2\dfrac{3}{4}\).
Solved Examples on Simplifying Fractions

Example 1: Sally loves growing flowers in her garden. Can you tell which flowers she grows the most? Express the part of those flowers in a form of the simplest fraction.
Solution:
The large area of the garden is filled with red flowers. So, Sally loves to grow red flowers the most. Red flowers cover 8/12 of her garden. Let's express the fraction 8/12 in its simplest form using the first method that we discussed. Factors of 8: 1, 2, 4, and 8. And, factors of 12: 1, 2, 3, 4, 6, and 12. Let's start dividing the numerator and denominator by 2, (8/2)/(12/2) = 4/6 = (4/2)/(6/2) = 2/3. Since 2 and 3 have no common factors except 1, 2/3 is the simplest form of 8/12. So, Sally loves growing red flowers the most. It is represented as 2/3.

Example 2: Jolly is playing with her magic disc. The disc is divided into 16 equal parts as shown. What part of the disc is colored blue? Can you express this fraction in the simplest form?
Solution
The fraction representing the blue shaded region in the disc is 8/16. Let's find the highest common factor of 8 and 16; factors of 8: 1, 2, 4, and 8, and factors of 16: 1, 2, 4, 8, and 16. We observe the highest common factor of 8 and 16 is 8. Let's divide the numerator and the denominator of 8/16 by the highest common factor, that is (8/8)/(16/8) = 1/2. This means half of the disc is colored blue. So, the simplest of 8/16 is 1/2.
Practice Questions on Simplifying Fractions
FAQs on Simplifying Fractions
What are the Steps to Simplify Fractions?
Follow the steps mentioned below to reduce a fraction to its simplest form:
 Find the highest common factor of the numerator and denominator.
 Divide the numerator and denominator by the highest common factor.
The fraction so obtained is in the simplest form.
How do you Simplify Large Fractions?
Large fractions can be simplified by dividing the numerator and denominator by the common prime factors to reduce it to the simplest form.
How do you Simplify Mixed Fractions?
Mixed fractions can be simplified using the formula given below:
{(Whole × Denominator) + Numerator}/(Denominator)
For example, \(5\dfrac{3}{7}\) = {(5 × 7) +3}/7 = 38/7
What is an Improper Fraction?
The fractions in which the numerator is bigger than the denominator are called improper fractions.
How to Convert an Improper Fraction to its Simplified Form?
Divide the numerator by denominator to obtain quotient and remainder. Then, the mixed fraction or the simplified fraction can be written as \(\text{Quotient}\dfrac{\text{Remainder}}{\text{Divisor}}\)
How are Fractions Reduced to their Lowest terms?
To reduce a fraction into its simplest form, divide the numerator and denominator by the highest common factor.
What is the Easiest way to Simplify a Fraction?
One of the quickest ways to reduce a fraction to its simplest form is to divide the numerator and denominator of the fraction by the highest common factor.
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