Proper Fractions, Improper Fractions and Mixed Numbers (Mixed Fractions)

What are Proper Fractions?
A proper fraction represents a quantity that is less than one whole. In a proper fraction, the numerator (the top number) is smaller than the denominator (the bottom number).
Example:
\(\frac{2}{3}, \frac{43}{100} \)

What are Improper Fractions?
An improper fraction represents a quantity that is equal to or greater than one whole. In an improper fraction, the numerator is equal to or larger than the denominator.
Example:
\(\frac{7}{4}, \frac{77}{68} \)

What are Mixed Numbers (Mixed Fractions)?
A mixed number is a way to express an improper fraction as a combination of a whole number and a proper fraction. It consists of a whole number part and a fractional part (which must be a proper fraction).
Example:
\(2\frac{3}{5} = \frac{13}{5} \)

The following diagrams show examples of proper fraction, improper fraction, and mixed number. Scroll down the page for more examples and solutions on proper fractions, improper fractions and mixed numbers.

 

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

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

 

This fun video will illustrate the different types of fractions

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Converting Between Improper Fractions and Mixed Numbers
A. Improper Fraction to Mixed Number

1. Divide numerator by denominator to get the whole number.
2. Write the remainder as a fraction.

B. Converting a Mixed Number to an Improper Fraction

1. Multiply the whole number part by the denominator of the fractional part.
   
2. Add the numerator of the fractional part to the product from Step 1. This sum becomes the new numerator.
3. The denominator stays the same as the original fractional part.

How to convert between improper fractions and mixed numbers?
Convert from Improper Fraction to Mixed Number
An improper fraction can be converted into a mixed number - first divide the numerator by the denominator. The resultant becomes the whole number, and the remainder becomes the numerator of the new fraction. The denominator of the new fraction is the same as the original denominator. If there is no remainder, then there is no fraction - the result is simply a whole number.

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Convert from Mixed Number to Improper Fraction
This following video will illustrate how to convert from a mixed number to an improper fraction

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