How to Write an Equivalent Fraction With a Given Denominator

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Fractions can appear different but still have the same value. Fractions that have different numerators and denominators but represent the same amount are called equivalent fractions. Equivalent fractions are fractions that are not reduced or simplified, and they are an important tool in evaluating and comparing proportions. To create an equivalent fraction, a fraction’s numerator and denominator can both be multiplied or divided by a single number. You can write an equivalent fraction with a given denominator by finding how that denominator relates to the other fraction.

    Write down a fraction and the denominator of the proposed equivalent fraction. For example, the fraction is 3/4 and the equivalent fraction's denominator be 80.

    Divide the new denominator into the original fraction's denominator. In this example, 80 divided by 4 equals 20.

    Multiply the quotient to the numerator of the original fraction, then write the product as the numerator over the equivalent fraction's denominator. Concluding this example, 20 multiplied by 3 equals 60, and 60 over 80 becomes 60/80.


    • As a check, divide the numerator by the denominator in both equations. If the fractions are equivalent, the quotient will be the same.


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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