Reduce Fractions
An important step that we do while we solve fraction problems is to reduce them to the simplest form. Though we reduce them to simplify, the value of the fraction is going to remain unchanged. The reduced fraction is equivalent to the original fraction. In fact, the original fraction and the reduced fractions form a pair of equivalent fractions. In this minilesson, we will learn how to reduce fractions using three different ways.
What are Reduce Fractions?
Reducing fractions means simplifying a fraction, wherein we divide the numerator and denominator by a common divisor until the common factor becomes 1. In other words, a fraction cannot be divided anymore by the same whole number other than 1. For example, consider the fraction 8/24. Here is the step by step process to reduce the fraction.
 Step 1: Write the factors of numerator and denominator. Factors of 8 are 1, 2, 4, and 8, and factors of 24 are 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 reduced form.
Let's start dividing by 2: (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
Let's have a look at the example given below. The first circle has 2 shaded parts out of 8 total parts, whereas the second circle has only one shaded part out of 4 total parts. It is to be noted that the shaded portion is the same in both circles. So we can conclude that 2 equal parts out of 8 equal parts are the same as 1 equal part out of 4 equal parts.
How do you Reduce a Fraction?
Find out a common factor of numerator and denominator. Repeat the process until there are no more common factors. For example, in the fraction, 10/20, 5 is a common factor of both 10 and 20. On dividing the numerator and denominator by 5, we get, 10/20 = (10 ÷ 5) / (20 ÷ 5) = 2/4. The fraction reduces to 2/4 in the first step. Now, 2 is a common factor of 2 and 4. Reducing the fraction further, (2 ÷ 2) / (4 ÷ 2) = 1/2
Methods of Reducing Fractions
Reducing a fraction means making a fraction as simple as possible. In order to find the reduced forms of fractions which just implies simplifying the fraction to its lowest form. Let us look at three easy methods of reducing the fractions.
Equivalent Fractions Method
Equivalent fractions have the same value irrespective of their numerators and denominators. Given below are the steps to reduce fractions by equivalent fractions method.
 Step 1: Find any common factor of both numerator and denominator.
 Step 2: Divide the numerator and denominator by the common factor.
 Step 3: Repeat the same step in the resulting fraction until there are no more common factors other than 1.
GCF Method
The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers. Given below are the steps to reduce fractions by the GCF method.
 Step 1: Find the greatest common factor (GCF) of numerator and denominator.
 Step 2: Divide the numerator and denominator by the GCF. The fraction so obtained is the reduced fraction.
Prime Factorization Method
Prime factorization is a way of expressing a number as a product of its prime factors. Given below are the steps to reduce fractions by the prime factorization method.
 Step 1: Find the prime factorization of both numerator and denominator.
 Step 2: Cancel out the common factors of the numerator and denominator.
 Step 3: Take away the remaining numbers in the numerator and denominator to find the reduced fraction.
Reducing Fractions on Number Line
We already know how to represent whole numbers on a number line. We can also show fractions on a number line. Fractions can be represented on a number line. To reduce any fraction we tend to find an equivalent fraction, with the numerator and the denominator having no common factor, except 1. To find out reducing fractions via number line we need to show many equivalent fractions and then decide on the reduced form of the given fraction. To mark an equivalent fraction on the number line, follow the below steps.
 Step 1: Draw a line that with two whole numbers marked at the ends.
 Step 2: Divide them into a number of equal parts as the denominator.
 Step 3: Find all the reduced forms of the fractions.
 Step 4: Identify the equivalent fractions.
How to Reduce Fractions with Variables?
Variables are letters like a, b, c, x, y, z, etc that appear in a mathematical expression and they represent unknown values. Fractions can have variables along with numbers. To reduce a fraction with variables, follow the steps given below:
 Step 1: Group the like terms together. For example, in the fraction (8a  a + 2a) / (12a). We group the like terms of a. On simplifying the numerator, we get 9a. The fraction now reduces to 9a /12a
 Step 2: Find the common factors and cancel them. 9a / 12a = (3 × 3 × a) / (3 × 4 × a). Canceling the common factors and simplifying, we get the fraction reduced to 3/4
Tips & Tricks on Reducing Fractions
So, now you know the three methods to reduce a fraction to its simplest form. Here are some tricks for you that will help you to reduce fractions quickly. Follow these tips and tricks while reducing fractions to their simplest form. Tips & tricks on reducing fractions are:
 If either numerator or denominator of a fraction is a prime number then the fraction cannot be simplified further.
 A fraction that has 1 in the numerator cannot be reduced further.
 To reduce an improper fraction, first, write it as a mixed fraction and follow the same method of simplifying a proper fraction.
Solved Examples

Example 1:Reduce the following fractions by the GCF method. a) 16/64, b) 18/81
Solution:
a) The greatest common factor of 16 and 64 is 16. Dividing both numerator and denominator by 16, we get the fraction reduced to 1/4. 16/64 = (16 ÷ 16) / (64 ÷ 16) = 1/4. Therefore, the reduced form of 16/64 is 1/4
b) The greatest common factor of 18 and 81 is 9. Dividing both numerator and denominator by 9, we get the fraction reduced to 2/9. 18/81 = (18 ÷ 9) / (81 ÷ 9) = 2/9. Therefore, the reduced form of 18/81 is 2/9

Example 2: Reduce the following fractions by the prime factorization method. a) 3/15, b) 20/60
Solution:
a) Let's find the prime factorization of 3 and 15. Prime factorization of 3 = 3 and Prime factorization of 15 = 3 × 5. Canceling out the common factors we get, 1/5. Therefore, the reduced form of 3/15 is 1/5
b) Let's find the prime factorization of 20 and 60. Prime factorization of 20 = 2 × 2 × 5 and Prime factorization of 60 = 2 × 2 × 3 × 5. Canceling out the common factors we get, 1/3. Therefore, the reduced form of 20/60 is 1/3

Example 3: Reduce the fraction (x^{2} + 5x + 6) / (x+3)^{2}
Solution:
The numerator x^{2} + 5x + 6 can be factorized as x^{2} + 5x + 6 = (x + 2) (x + 3). Now, (x^{2} + 5x + 6) / (x+3)^{2} = (x + 2) (x + 3) / (x+3)^{2}. Cancelling out the common factors we get, (x + 2) / (x + 3). Therefore, educed form of the fraction (x^{2} + 5x + 6) / (x+3)^{2 } is (x + 2) / (x + 3)
Example 4: Richard bought a largesized pizza and cut it into 12 slices. He ate fourtwelfth of the pizza and gave the rest to his brother. Find the fraction of pizza eaten by Richard and his brother. Express both answers in the reduced form.
Solution:
The fraction of pizza eaten by Richard = 4/12. Since 4 is the greatest common factor of 4 and 12, on reducing the fraction we get, 1/3. The fraction of pizza eaten by his brother = 1  1/3 = 2/3. Therefore, the fraction of pizza eaten by Richard and his brother is 2/3
Practice Questions
FAQs on Reduce Fractions
How do you Reduce Large Fractions?
In order to reduce large fractions, divide the numerator and denominator of the large fraction by the common prime factors to reduce it to the simplest form.
How do you Reduce Mixed Fractions?
Mixed fractions can be reduced using the formula: \(\dfrac{(\text{Whole}\times\text{Denominator})+\text{Numerator}}{\text{Denominator}}\). For example, \(5\dfrac{3}{7}=\dfrac{(5\times 7)+3}{7}=\dfrac{38}{7}\).
What are the Steps to Reduce 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 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 Reduce 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.
What is an Improper Fraction?
A fraction that has its numerator greater than its denominator is called an improper fraction. For example, 7/4
How to Convert An Improper Fraction to A Mixed Fraction?
To convert an improper fraction to a mixed number, we divide the numerator by denominator. Write the quotient, and also write the remainder above the denominator next to the quotient.
How do you Reduce Fractions with Exponents?
To reduce fractions with exponents, apply the power of the exponent to both the numerator and the denominator. For example, (a/b)^{n} = a^{n}/b^{n } where 'a' and 'b' are the numerator and denominator respectively and 'n' is the exponent of the fraction. After evaluating the fraction with the power, reduce the fraction to its simplest form.