How to Add Fractions with Mixed Numbers

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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.

Common Denominators

    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.

    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.

    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.

    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.

Different Denominators

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

    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.

    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.

    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.

    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.

    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.

    Tips

    • If adding two mixed numbers, add the integer parts of the numbers together before the first step for both sections.

References

About the Author

Chance E. Gartneer began writing professionally in 2008 working in conjunction with FEMA. He has the unofficial record for the most undergraduate hours at the University of Texas at Austin. When not working on his children's book masterpiece, he writes educational pieces focusing on early mathematics and ESL topics.

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