How to Simplify Mixed Fractions

Mixed fractions, also known as mixed numbers, consist of a whole number and a proper fraction combined. Simplifying mixed fractions is an essential skill in mathematics, as it helps to make calculations and comparisons easier. In this guide, we’ll take you through the process of simplifying mixed fractions step by step. With practice, you’ll be able to simplify mixed fractions in no time!

How to Simplify Mixed Fractions

Step 1: Identify the Mixed Fraction

A mixed fraction is a number that consists of a whole number and a proper fraction. For example, 2 1/2 is a mixed fraction, with 2 as the whole number and 1/2 as the proper fraction.

Step 2: Simplify the Proper Fraction (If Necessary)

Before we can simplify the mixed fraction, we need to simplify the proper fraction (if possible). To do this, find the greatest common divisor (GCD) of the numerator and the denominator. Then, divide both the numerator and the denominator by the GCD.

For example, let’s simplify the fraction 8/12:

1. Find the GCD of 8 and 12, which is 4.
2. Divide both the numerator and the denominator by the GCD: 8 ÷ 4 = 2 and 12 ÷ 4 = 3.
3. The simplified fraction is 2/3.

Step 3: Convert the Mixed Fraction to an Improper Fraction

An improper fraction has a numerator that is greater than or equal to its denominator. To convert a mixed fraction to an improper fraction, follow these steps:

1. Multiply the whole number by the denominator of the proper fraction.
2. Add the numerator of the proper fraction to the result obtained in step 1.
3. Write the result from step 2 as the new numerator, keeping the same denominator.

For example, let’s convert the mixed fraction 2 2/3 to an improper fraction:

1. Multiply the whole number by the denominator: 2 × 3 = 6.
2. Add the numerator of the proper fraction: 6 + 2 = 8.
3. Write the new numerator with the same denominator: 8/3.

Step 4: Simplify the Improper Fraction (If Necessary)

If the improper fraction can be simplified further, repeat step 2 to find the GCD of the numerator and the denominator, and then divide both by the GCD.

For example, let’s simplify the improper fraction 9/12:

1. Find the GCD of 9 and 12, which is 3.
2. Divide both the numerator and the denominator by the GCD: 9 ÷ 3 = 3 and 12 ÷ 3 = 4.
3. The simplified fraction is 3/4.

Step 5: Convert the Improper Fraction Back to a Mixed Fraction

To convert the simplified improper fraction back to a mixed fraction, follow these steps:

1. Divide the numerator by the denominator, noting the quotient and the remainder.
2. Write the quotient as the whole number and the remainder as the numerator of the proper fraction, keeping the same denominator.

For example, let’s convert the improper fraction 8/3 back to a mixed fraction:

1. Divide the numerator by the denominator: 8 ÷ 3 = 2 with a remainder of 2.
2. Write the quotient as the whole number and the remainder as the numerator of the proper fraction: 2 2/3.

Now you have successfully simplified the mixed fraction!