How to Divide Fractions With Ease

To invert fractions, turn it over so the numerator and denominator switch places.
••• Comstock Images/Comstock/Getty Images

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.


    • 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.

Related Articles

Tricky Math Questions
Step by Step Instructions on Math Fractions
How to Estimate Sum & Differences With Fractions
How to Divide Fractions With Different Denominators
How to Find a Fraction of a Number
How to Multiply 3 Fractions
How to Convert a Fraction to a Ratio
How to: Improper Fractions Into Proper Fractions
How to Do Fractions on a TI-30X IIS
How to Write a Rational Number as the Quotient of Two...
How to Calculate 2/3 of a Number
How to Find the X Intercept of a Function
How to Add & Subtract Improper Fractions
How to Convert a Decimal to a Whole Number
How to Multiply Fractions by Percentages
How to Estimate Division Problems
Adding & Subtracting Fractions
How to Factorise a Quadratic Expression
How to Write an Equivalent Fraction With a Given Denominator
How to Divide Negative Fractions