How to Divide Fractions With Ease

To invert fractions, turn it over so the numerator and denominator switch places.
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If fractions have you all tied up in knots, wondering how to divide fractions with ease, the good news is this: if you you can multiply you can divide fractions. As long as you know that a reciprocal fraction is just a fraction turned upside down so that, for instance, 3/4 becomes 4/3, and that a whole number over one is equal to the whole number, such as 5 equals 5/1, then dividing fractions should be a breeze. To divide mixed number fractions, you will have to convert it to an improper fraction before proceeding with the simple division algorithm. A few practice problems and you will be a master at dividing fractions without blinking an eyelash.

Simple Fractions

    Read the fraction division problem such as 3/4 ÷ 5/8. Invert the second fraction to form the reciprocal so 5/8 becomes 8/5.

    Rewrite the first fraction and the reciprocal of the second as a multiplication sentence 3/4 x 8/5.

    Multiply the numerators together, then the denominators: 3 x 8 is 24 and 4 x 5 is 20. Therefore, the answer is 24/20.

    Reduce the answer to lowest terms. 24 ÷ 20 equals 1 4/20. The greatest common factor (GCF) of 4 and 20 is 4 so divide the numerator and denominator by the GCF to simplify it and find the final answer, 1 1/5.

Fractions and Whole Numbers

    Read a fraction division problem such as 9/15 ÷ 3. Write 3 as 3/1 and invert to get 1/3 as the reciprocal.

    Write the equation 9/15 x 1/3.

    Multiply the numerators and denominators: 9 x 1 is 9 and 15 x 3 is 45 making the product 9/45.

    Find the GCF of 9 and 45, which in this case is 9. Divide both numbers by 9 to find the final, simplified answer: 1/5.

Mixed Numbers

    Read a fraction division problem such as 8 1/9 ÷ 5/10. Convert the mixed number to an improper fraction by multiplying the denominator by the whole number, 9 x 8 is 72. Add the numerator, 72 + 1 is 73. The denominator remains the same so 8 1/9 equals 73/9.

    Invert the second fraction so 5/10 becomes 10/5.

    Rewrite the equation as a multiplication sentence with the improper fraction and the reciprocal, 73/9 x 10/5.

    Multiply the numerators and denominators: 73 x 10 equals 730 and 9 x 5 equals 45 so the product is 730/45.

    Divide the numerator by the denominator. The remainder is the numerator in the resulting mixed number, 16 10/45. Divide the new numerator and denominator by the GCF to reduce the fraction to lowest terms. The GCF of 10 and 45 is 5 so the final answer is 16 2/9.

    Tips

    • For a tutorial on finding the greatest common factor to help reduce fractions to lowest terms, try Math Playground's "Factor Trees" exercise or AAA Math's drills.

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