How to Write a Mixed Number as an Improper Fraction

A mixed number is a combination of a whole number and a proper fraction. Here we will learn how to convert a mixed number into an improper fraction. Here is the answer of the same.

To write a mixed number as an improper fraction, we need to multiply the whole number with the denominator of the proper fraction and then add the numerator of the proper fraction to this product. The desired improper fraction is obtained by taking this sum as its numerator and the denominator of the proper fraction as its denominator.

Let us now learn this process of converting a mixed number into an improper fraction step-by-step with the help of examples.

Steps to Convert a Mixed Number into an Improper Fraction

Note that a mixed number consists of a whole number and a proper fraction, that is, it has the form:

Mixed number = (whole number)$\dfrac{\text{numerator}}{\text{denominator}}$.

In order to write a mixed number as an improper fraction, we have to follow the steps listed here:

1. First, multiply the whole number and the denominator.
2. To this product, add the numerator of the proper fraction.
3. The sum obtained in the second step will be the numerator of the improper fraction where as its denominator will be the same as the denominator of the proper fraction.

Read Also: Similar and dissimilar fractions: Definition, Addition, Conversion

Examples

We now understand the above method of converting a mixed number into an improper fraction with an example.

Example 1: Convert the mixed number $3 \dfrac{1}{2}$ into an improper fraction.

Solution:

Multiply 3 and 2, and then add 1 to this product.

So the sum = (3×2) +1 = 6+1 =7.

Thus, by the above rule,

Numerator = 7

Denominator = 2.

So the mixed number $3 \dfrac{1}{2}$ as an improper fraction is equal to $\dfrac{7}{2}$.

Example 2: Convert the mixed number $2 \dfrac{10}{11}$ into an improper fraction.

Solution:

Multiply 2 and 11, and then add 10 to this product.

So this sum = (2×11) +10 = 22+10 =32.

Hence using the above rule, the improper fraction is determined as follows:

Numerator = 32

Denominator = 11.

So the mixed number $2 \dfrac{10}{11}$ as an improper fraction is $\dfrac{32}{11}$.

Also Read:

• Like and Unlike fractions
• Simple surds and compound surds

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