Mixed Number to Improper Fraction Calculator

This calculator converts any mixed number (fraction) into an improper fraction and gives you the answer in simplest form. Just enter the mixed fraction and click the “Convert” button to get instant results with step-by-step explanation.

Want to turn an improper fraction back into a mixed number? Use the Improper Fraction to Mixed Number Calculator now!

How to Use the Mixed Number to Improper Fraction Calculator

Converting any mixed number to an improper fraction using this calculator is very straightforward. Just follow these steps:

1. Enter the mixed number
2. Click the “Convert” button

The calculator will display the improper fraction and show you exactly how the mixed number was converted to an improper fraction.

What is a Mixed Number?

A mixed number, also known as a mixed fraction, is a number that combines a whole number and a proper fraction. It is used to represent quantities that are greater than one but are not whole numbers. For instance, $2\frac{1}{3}$ is a mixed fraction, where 2 is the whole number, and $\frac{1}{3}$ is the proper fraction part.

What is an Improper Fraction?

An improper fraction is a type of fraction where the numerator (top number) is greater than or equal to the denominator (bottom number). Examples of improper fractions include $\frac{11}{4}$, $\frac{11}{11}$, $\frac{9}{2}$, etc. Understanding the difference between improper and proper fractions helps you compare fractions.

How to Turn a Mixed Number into an Improper Fraction

Struggling with turning mixed numbers to improper fractions? You only need to master the general formula. The general formula for converting any mixed number into an improper fraction is:

However, if you prefer steps to mastering the formula, then you only need to follow these steps to change from a mixed number to an improper fraction:

1. Multiply the whole number by the denominator.
2. Add the numerator of the fractional part to the product from Step 1. This sum becomes the new numerator for the improper fraction.
3. Keep the old denominator and write the improper fraction

Example 1

Convert the mixed number $3\frac{2}{5}$ into an improper fraction.

Solution:

Step 1: Multiply the whole number by the denominator.

The whole number is 3, and the denominator is 5.

Multiplying the whole number by the denominator, we have:

3×5=15

Step 2: Add the numerator of the fractional part to the product from Step 1.

The result from Step 1 is 15, and the numerator part of the proper fraction is 2.

Adding these two numbers, we get:

15+2=17

This becomes the new numerator of the improper fraction

Step 3: Keep the old denominator and write the improper fraction

Retaining the old denominator (5), we can now write the mixed number into an improper fraction as follows:

new numerator (17)/old denominator (5)

Therefore, converting $3\frac{2}{5}$ into an improper fraction becomes $\frac{17}{5}$.

Similarly, the online calculator yields similar results as shown below:

Example 2

Convert $4\frac{3}{7}$ to an improper fraction.

Solution:

Step 1: Multiply the whole number by the denominator.

From the question, the whole number is 4, and the denominator is 7

Multiplying the whole number by the denominator gives:

4×7 = 28

Step 2: Add the numerator to the result.

The old numerator is 3, and the result in step 1 is 28. Adding the old numerator to the result in step 1 gives:

28+3=31

This forms the new numerator.

Step 3: Keep the old denominator and write the improper fraction

The resulting improper fraction is given by:

New numerator (31)/Old denominator (7)

Therefore, converting $4\frac{3}{7}$ into an improper fraction gives $\frac{31}{7}$.

Similarly, using the calculator, converting $4\frac{3}{7}$ into an improper fraction yields similar results as shown below: