Help with Mixed Fractions: Division and Measurements

Dividing with mixed fractions is an advanced fraction skill that you'll learn near the end of elementary school. Keep reading for mixed fraction help!

Find available tutors

Mixed Fractions

A mixed fraction combines a whole number, like one, three or eight, with a fraction, like 1/2, 2/3 or 7/8. You might use a fraction to show that your family drank 2 1/2 (two and one half) gallons of milk this week, or you ran 1 3/4 (one and three-quarters) of a mile.


Mixed fractions are commonly used for measurements that contain a number of whole units, as well as a fractional unit. For instance, you might measure a piece of paper that's between five and six inches long. On a ruler, the space between five and six inches will be divided into fractions: 1/8, 1/4, 3/8, 1/2 and so on. You'll express the paper's length as the lower whole number (five) and the nearest fraction, such as 5 3/8 or 5 3/4.


Improper Fractions

Dividing mixed fractions is only possible if you turn the mixed fraction into an improper fraction. This is simply a fraction with a numerator that's larger than the denominator. To make this conversion, follow these steps:

1. Multiply the mixed fraction's denominator by the whole number. For instance, if the mixed fraction is 4 3/7, multiply 7 x 4.
2. Add that product to the mixed fraction's numerator. The result becomes the numerator of the answer. For example, 7 x 4 = 28, and 28 + 3 = 31, so 31 is the answer's numerator.
3. Write the new numerator over the denominator from the mixed fraction. For example, 4 3/7 = 31/7.

Multiplying Reciprocals

Now that you can change mixed fractions into improper fractions, the next step is to divide them. Dividing any fraction, including an improper fraction, involves multiplying one fraction by the reciprocal of the other one. To get the reciprocal, just reverse the numerator and the denominator. For instance, 3/4 becomes 4/3.

To solve your division problem, convert the mixed fraction to an improper fraction first. For instance, 4 1/2 becomes 9/2. Then, if you're dividing by a fraction, like 1/3, find its reciprocal (3/1). Last, you'll just multiply those two fractions together to get 27/2. Here's the step-by-step process:

4 1/2 ÷ 1/3

= 9/2 ÷ 1/3

= 9/2 x 3/1

= 27/2

Did you find this useful? If so, please let others know!

Other Articles You May Be Interested In

We Found 7 Tutors You Might Be Interested In

Huntington Learning

  • What Huntington Learning offers:
  • Online and in-center tutoring
  • One on one tutoring
  • Every Huntington tutor is certified and trained extensively on the most effective teaching methods
In-Center and Online


  • What K12 offers:
  • Online tutoring
  • Has a strong and effective partnership with public and private schools
  • AdvancED-accredited corporation meeting the highest standards of educational management
Online Only

Kaplan Kids

  • What Kaplan Kids offers:
  • Online tutoring
  • Customized learning plans
  • Real-Time Progress Reports track your child's progress
Online Only


  • What Kumon offers:
  • In-center tutoring
  • Individualized programs for your child
  • Helps your child develop the skills and study habits needed to improve their academic performance
In-Center and Online

Sylvan Learning

  • What Sylvan Learning offers:
  • Online and in-center tutoring
  • Sylvan tutors are certified teachers who provide personalized instruction
  • Regular assessment and progress reports
In-Home, In-Center and Online

Tutor Doctor

  • What Tutor Doctor offers:
  • In-Home tutoring
  • One on one attention by the tutor
  • Develops personlized programs by working with your child's existing homework
In-Home Only


  • What TutorVista offers:
  • Online tutoring
  • Student works one-on-one with a professional tutor
  • Using the virtual whiteboard workspace to share problems, solutions and explanations
Online Only

Our Commitment to You

  • Free Help from Teachers

  • Free Learning Materials

  • Helping Disadvantaged Youth