Improper Fractions

Understanding improper fractions and mixed numbers is an important part of learning fractions.

What are improper fractions?
An improper fraction is a fraction where the numerator (top number) is greater than the denominator (bottom number). The fraction \(\frac{a}{b}\) is an improper fraction if a > b.

Examples: \(\frac{5}{3}, \frac{7}{2}, \frac{11}{4}\)

An improper fraction represent a quantity that is more than one whole. For example, \(\frac{5}{3}\) means you have five “thirds.”

The following diagram shows an example of improper fraction and its equivalent mixed number. Scroll down the page for more examples and solutions on how to convert between improper fraction and mixed number.

 

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What are mixed numbers?
A mixed number is a combination of a whole number and a proper fraction (where the numerator is smaller than the denominator).

Examples: \(1\frac{2}{3}, 3\frac{1}{2}, 2\frac{3}{4}\)

Mixed numbers has the same quantities as improper fractions but in a different format. For example, \(1\frac{2}{3}\) means you have one whole and two-thirds.

Converting Improper Fractions to Mixed Numbers
To convert an improper fraction to a mixed number:

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.

Example:
Convert \(\frac{7}{3}\) to a mixed number.

1. Divide 7 by 3: 7÷3 = 2 with a remainder of 1.
2. Write the mixed number: \(2\frac{1}{3}\)

Converting Mixed Numbers to Improper Fractions
To convert a mixed number to an improper fraction:

1. Multiply the whole number by the denominator.
2. Add the numerator to the result.
3. Write the total as the new numerator over the original denominator.

Example:
Convert \(2\frac{1}{3}\) to an improper fraction.

1. Multiply 2 by 3: 2×3=6.
2. Add 1: 6+1=7.
3. Write the improper fraction: \(\frac{7}{3}\).

Improper Fractions & Mixed Numbers Videos
What’s an improper fraction?
How to convert between improper fraction and mixed number?

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Proper fractions, improper fractions, and mixed numbers
Learn how to convert improper fractions to and from mixed number.

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Proper Fraction, Improper Fraction & Mixed Number songs
Songs to help you remember how to convert between improper fraction and mixed number.

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