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., \(2\frac{3}{4}\)), while an improper fraction has a numerator larger than or equal to its denominator (e.g., \(\frac{11}{4}\)).

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.

 

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

Converting a Mixed Number to an Improper Fraction
To convert a mixed number to an improper fraction, follow these steps:

1. Multiply the whole number by the denominator.
   
2. Add the numerator to the result from step 1.
   
3. Write the sum over the original denominator.
   

Converting an Improper Fraction to a Mixed Number
To convert an improper fraction to a mixed number, follow these steps:

1. Divide the numerator by the denominator to get the whole number part.
   
2. Write the remainder as the new numerator over the original denominator.
   

Free Fraction Games
Learning Fractions	Equivalent Fractions	Compare Fractions
Simplify Fractions	Greatest Common Factor	Least Common Multiple
Improper Fractions & Mixed Numbers	Add Fractions	Subtract Fractions
Subtract Fractions from Whole Numbers	Multiply Fractions	Divide Fractions
Multiply Fractions & Whole Numbers	Divide Fractions & Whole Numbers	Add Mixed Numbers
Subtract Mixed Numbers	Multiply Mixed Numbers	Divide Mixed Numbers

 

Videos

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

• Show Video Lesson

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

• Show Video Lesson

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

• Show Video Lesson

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

• Show Video Lesson

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

• Show Video Lesson

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

• Show Video Lesson

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

• Show Video Lesson

Try out our new and fun Fraction Concoction Game.

Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.

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