Mixed Numbers and Improper Fractions

Converting between mixed numbers and improper fractions is a fundamental skill in math. A mixed number consists of a whole number and a proper fraction (e.g., 2 3/4), while an improper fraction has a numerator larger than or equal to its denominator (e.g., 11/4).

The following diagrams show how to convert a mixed number to an improper fraction. Scroll down the page for more examples and solutions.

 

The following diagrams show how to convert an improper fraction to a mixed number. Scroll down the page for more examples and solutions.

 

1. Converting a Mixed Number to an Improper Fraction
   To convert a mixed number to an improper fraction, follow these steps:
   Multiply the whole number by the denominator.
   Add the numerator to the result from step 1.
   Write the sum over the original denominator.
   

2. Converting an Improper Fraction to a Mixed Number
   To convert an improper fraction to a mixed number, follow these steps:
   Divide the numerator by the denominator to get the whole number part.
   Write the remainder as the new numerator over the original denominator.
   

Fraction Worksheets
Practice your skills with the following fraction worksheets.
Online & Printable Fraction Worksheets

Converting a Mixed Number to an Improper Fraction
Examples:
Write the mixed number as an improper fraction
a) 1 5/7
b) 3 1/8

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Convert an Improper Fraction to a Mixed Number
Examples:
a) 8/5
b) 31/9

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Mixed numbers and improper fractions
Converting mixed numbers to improper fractions and improper fractions to mixed numbers.
Examples:
a) Convert to improper fraction.
2 1/2
b) Convert to mixed number.
23/5

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Changing improper fractions into mixed numbers
Examples:
10/7
23/10

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Change mixed numbers into improper fractions
Examples:
1 3/4
3 3/5

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Converting an Improper Fraction into a Mixed Number
Example:
Change to Mixed Number
9/4

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Converting a Mixed Number into an Improper Fraction
Example:
2 3/4

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Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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