How to Divide Fractions

Mathematicians didn’t want to muck up fraction division by making you do something as complicated as actually dividing, so they devised a way to use multiplication instead. To divide one fraction by another fraction, change the problem to multiplication:

  1. Change the division sign to a multiplication sign.

  2. Change the second fraction to its reciprocal.

    Switch around the numerator (top number) and denominator (bottom number).

  3. Solve the problem using fraction multiplication.

When dividing fractions, you may have to reduce your answer or change it from an improper fraction to a mixed number.

Sample questions

  1. Divide 5/8 by 3/7.

    image0.jpg

    Change the division to multiplication:

    image1.jpg

    Solve the problem using fraction multiplication:

    image2.jpg

    The answer is an improper fraction (because the numerator is greater than the denominator), so change it to a mixed number. Divide the numerator by the denominator and put the remainder over the denominator:

    image3.jpg
  2. Solve

    image4.jpg image5.jpg

    Change the division to multiplication:

    image6.jpg

    Notice that you have a 5 in one of the numerators and a 10 in the other fraction’s denominator, so you can cancel out the common factor, which is 5; that would change your problem to

    image7.jpg

    Or you can simply do your calculations and reduce the fraction later, as I do here. Solve by multiplying these two fractions:

    image8.jpg

    This time, the numerator and denominator are both divisible by 5, so you can reduce them:

    image9.jpg

    Because the numerator is greater than the denominator, the fraction is improper, so change it to a mixed number:

    1-3/4

Practice questions

  1. Divide 1/4 by 6/7.

  2. Find

    image10.jpg
  3. Divide 8/9 by 3/10.

  4. Solve

    image11.jpg

Following are answers to the practice questions:

  1. image12.jpg

    First, change the problem to multiplication, multiplying by the reciprocal of the second fraction:

    image13.jpg

    Now complete the problem using fraction multiplication:

    image14.jpg
  2. image15.jpg

    Change the problem to multiplication, using the reciprocal of the second fraction:

    image16.jpg

    Complete the problem using fraction multiplication:

    image17.jpg

    Both the numerator and denominator are divisible by 5, so reduce the fraction by this factor:

    image18.jpg

    They’re still both divisible by 3, so reduce the fraction by this factor:

    image19.jpg
  3. image20.jpg

    Change the problem to multiplication, using the reciprocal of the second fraction:

    image21.jpg

    Complete the problem using fraction multiplication:

    image22.jpg

    The numerator is greater than the denominator, so change this improper fraction to a mixed number:

    image23.jpg
  4. image24.jpg

    Change the problem to multiplication, using the reciprocal of the second fraction:

    image25.jpg

    Complete the problem using fraction multiplication:

    image26.jpg

    The numerator is greater than the denominator, so change this improper fraction to a mixed number:

    image27.jpg

    Now the numerator and the denominator are both divisible by 3, so reduce the fractional part of this mixed number by a factor of 3:

    image28.jpg

    The numerator and denominator are now both divisible by 7, so reduce the fractional part by this factor:

    image29.jpg
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