$Colorful House of Math logo$

Algebra

Geometry

Statistics and Probability

Functions

Proofs

Encyclopedia>Numbers and Quantities>Fractions and Percentages>About Fractions>Proper Fraction, Improper Fraction and Mixed Fraction

Video Crash Courses

Want to watch animated videos and solve interactive exercises about different types of fractions? Click here to try the Video Crash Course called “What Is a Fraction?”!

A fraction consists of a numerator (top), a denominator (bottom) and a fraction bar separating the two numbers. We have two different types of fractions: proper fractions and improper fractions. Additionally, we can write an improper fraction as a mixed fraction. Here, we’re going to look at the three different types of fractions.

Proper Fraction

$Three examples of proper fractions$

Rule

A fraction where the numeric value in the numerator is less than the numeric value in the denominator is called a proper fraction.

Improper Fraction

$Three examples of improper fractions$

Rule

A fraction where the numeric value in the numerator is larger than, or equal to the numeric value in the denominator is called an improper fraction.

Mixed Fraction

$Two examples of mixed fractions$

Rule

An improper fraction can be written using an integer together with a fraction. We call this a mixed fraction or mixed number.

Think About This

Can you see how to change a mixed fraction into an improper fraction?

You multiply the number in the denominator with the large number. Next, you add the numerator. The answer to that is the numerator in the improper fraction. The denominator stays the same:

\begin{array}{l} 2 \frac{1}{4} = \frac{2 \cdot 4}{4} + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{8 + 1}{4} = \frac{9}{4} \end{array}

Think About This

Can you see how to change an improper fraction into a mixed number?

First, you ask: How many times does the denominator go into the numerator? In this case, the answer is $2$ , because $4 \cdot 2 = 8$ . Next, you ask: When the integer is separated from the fraction, how many shares do you have left? In this case, the answer is $9 - 8 = 1$ , which makes the fraction in the mixed number $\frac{1}{4}$ . The calculation looks like this: