How to Add Similar & Dissimilar Fractions

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Adding similar fractions is easy, but adding dissimilar ones requires an additional step. Before you begin, you must know a few important key terms. First, the number on the top of a fraction is called the numerator, while the number on the bottom of a fraction is called the denominator. Similar fractions have the same denominator, also called a common denominator. To add dissimilar fractions (fractions with different denominators), you must first convert the fractions so that the denominators are the same.

    Multiply both parts of each fraction by the denominator of the other fraction, if the denominators are different. For example, if you are adding 1/3 and 2/5, multiply both 1 and 3 by 5, making the fraction 5/15. Then multiply both 2 and 5 by 3 (the denominator of the other fraction), making the fraction 6/15.

    Make the previous step easier if one of the denominators is a multiple of the other. For example, if you are adding 1/2 and 3/12, 12 is a multiple of 2 (2 x 6 = 12). In this case, leave 3/12 as is. Multiply both parts of 1/2 by 6 so that the denominator will be 12, making the fraction 6/12.

    Add the numerators, but leave the denominator the same, once you have similar fractions. For example, 5/15 + 6/15 = 11/15 or 6/12 + 3/12 = 9/12.

    Simplify the answer, if necessary. The fraction 11/15 cannot be simplified, but 9/12 can be simplified to 3/4 by dividing both the numerator and denominator by 3. If the numerator and denominator cannot both be divided by the same number, the fraction cannot be simplified.

    Check your work.


    • When converting fractions or finding equivalent fractions, always do the same thing to the numerator and the denominator.


About the Author

Elizabeth Earne is a writer and teacher. Her writing has appeared in "San Diego Family Magazine" and on various websites, with a focus on education, parenting and travel. Earne has taught writing to children for more than five years. She holds a Bachelor of Arts, as well as certification in cross-cultural language and academic development (CLAD).