How To Add Fractions With Mixed Numbers

A fraction is just one part of a mixed number. A mixed number is the result of adding a fraction to an integer. Mixed numbers are the proper form of improper fractions, or fractions that have a greater numerator, or top number, than denominator, or bottom number. Mixed numbers follow mathematical rules that are a combination of rules for integers and fractions. Adding fractions with mixed numbers aids in the understanding of addition rules for different types of numbers.

Step 1

Separate the fraction of the mixed number from its integer. For this example, the mixed number is 3 2/3. The fraction is 2/3.

Step 2

Add the numerators together and make that sum the numerator. For the example, the fraction to be added is 2/3. Adding the numerators 2 and 2 results in 4. The fraction becomes 4/3.

Step 3

Convert any improper fractions to a mixed number. Divide the denominator into the numerator, and place any remainder as the new numerator, combining the fraction with the integer. For the example, 4 divided by 3 equals 1 with a remainder of 1. 1 over 3 becomes 1/3, and 1/3 added to 1 equals 1 1/3.

Step 4

Add the integer of the mixed number to the integer in the first step, and then add the fraction. For the example, 3 plus 1 is 4, and 4 plus 1/3 equals 4 1/3.

Step 1

Separate the fraction of the mixed number from its integer. For example, the mixed number is 2 1/2. The fraction is 1/2.

Step 2

Multiply the mixed number's numerator and denominator by the denominator of the fraction being added. For the example, the fraction being added is 2/3. Multiplying 1 by 3 equals 3, and multiplying 2 by 3 equals 6. The fraction is now 3/6.

Step 3

Multiply the second fraction's numerator and denominator by the mixed number's original denominator. For the example, 2 multiplied by 2 equals 4, and 2 multiplied by 3 equals 6. The fraction becomes 4/6.

Step 4

Add the numerators together, and then place the sum as the numerator over the common denominator. For the example, 3 plus 4 equals 7, and 7 over 6 equals 7/6.

Step 5

Convert any improper fractions to a mixed number. Divide the denominator into the numerator, and place any remainder as the new numerator, combining the fraction with the integer. For the example, 7 divided by 6 equals 1 with a remainder of 1. 1 over 6 becomes 1/6, and 1/6 added to 1 equals 1 1/6.

Step 6

Add the integer of the mixed number to the integer from the first step, and then add the fraction to that sum. For the example, 2 plus 1 equals 3, and 3 plus 1/6 equals 3 1/6.