Types of Fractions

There are three different types of fractions, and here you will learn what they are. There are proper fractions, improper fractions, and mixed numbers.

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

A fraction where the numerical value in the numerator is greater than the numerical value in the denominator is called an improper fraction.

An improper fraction can also be expressed as an integer together with a fraction. We call this a mixed number.

Do you see how to convert from a mixed number to an improper fraction?

You multiply the number in the denominator by the integer—the big number—then add it to the numerator. The answer you get is the numerator in the improper fraction. The denominator stays the same:

$$\begin{array}{llll}\hfill 2\frac{1}{4}& =\frac{2\times 4}{4}+\frac{1}{4}& \hfill & \\ \hfill & =\frac{8}{4}+\frac{1}{4}& \hfill & \\ \hfill & =\frac{8+1}{4}& \hfill & \\ \hfill & =\frac{9}{4}& \hfill & \end{array}$$

Do you see how to convert from an improper fraction to a mixed number?

First you ask the question: How many times does the denominator go into the numerator? In this case, the answer is 2 because $4\times 2=8$. The answer to the multiplication operation must be less than or equal to the value of the numerator.

Then you ask: When the integers are counted, what’s the remainder—or put another way, how many parts are there left? In this case, the answer is $9-8=1$. The fraction in the mixed number is $\frac{1}{4}$. The calculation looks like this:

$$\frac{9}{4}=\frac{4}{4}+\frac{4}{4}+\frac{1}{4}=1+1+\frac{1}{4}=2\frac{1}{4}$$