Improper Fraction to Mixed Number Calculator

Created by Hanna Pamuła, PhD
Reviewed by Dominik Czernia, PhD and Jack Bowater
Last updated: Feb 02, 2023

Welcome to the improper fraction to mixed number calculator - a tool that lets you convert an improper fraction to a mixed number in the blink of an eye. In the short article below, you'll learn the basics - such as what an improper fraction is and the step-by-step instructions on how to turn an improper fraction into a mixed number. To do the opposite task, visit our mixed number to improper fraction calculator.

Since you're already here, peeking 👀 at this improper fraction to mixed number calculator, we suspect you may be interested in other fraction topics. For that reason, we've built a comprehensive fractions calculator that can deal with seven basic fraction operations. If you simply want to do the opposite task to this tool

What is an improper fraction? Improper fraction definition

To talk about improper fraction definition, we need to start with a bit of revision - what is a fraction, in general?

💡 A fraction tells us how many equal parts of a whole thing we have. We write it as a ratio of whole numbers separated by a line or a slash.

We call the top number the numerator and the bottom one the denominator.

Image explaining what a fraction is, on the example of slice of a cake. 1 as numerator, 6 as denominator

So in the above example, we have 1 part out of 6 - 1/6 read as one-sixth.

Now we can return to our central question: what is an improper fraction? According to the definition:

💡 A fraction is improper when the numerator is larger than (or equal to) the denominator.

As the numerator is equal to or greater than the bottom number, we sometimes call the improper fraction a top-heavy fraction. Examples of improper fractions are:

  • 🍰 10 slices of a cake, when each cake was cut into 6 slices;

  • 🍫 8 rows of the chocolate bar, when the whole chocolate bar has 5 rows;

  • 🍊 21 parts of orange, if we cut each orange into 8 equal pieces.

Image explaining what an improper fraction is. 10/6 of a pie, 8/5 of a chocolate bar, 21/8 of an orange

How to turn an improper fraction into a mixed number?

So, what does converting improper fractions to mixed numbers mean? All in all, a mixed fraction is just another way of expressing an improper fraction. But how does it work?

Look at the previous image again. In each of these examples, we have more than one whole thing, right? So, for example, instead of saying we have 8 rows of chocolate (and each bar has 5 rows), we could say - hey, I've one whole chocolate bar and an additional 3 parts out of 5. And that's just how converting improper fractions to mixed numbers works!

Image explaining conversion from improper fractions to mixed numbers. 8/5 of a chocolate bar is the same as 1 3/5

Let's go through our example step-by-step to see how to turn an improper fraction into a mixed number:

  1. Divide the numerator by the denominator (the top number by the bottom number).

    If you divide 8 by 5, you get a quotient (whole number) and a remainder:

    ⁸⁄₅ = 1 remainder 3 = 1 R 3

    (learn how to do it with the remainder calculator)

  2. Find the whole part of the mixed number - take the whole number from the division:

    1

  3. Find the fractional part of the mixed number - the remainder from the division is the new numerator, while the denominator stays the same:

  4. To get the mixed number, put the numbers together:

    1 ⅗

And that's it, ⁸⁄₅ = 1 ⅗

Sometimes you should also simplify the mixed fraction, but that's not the case here.

Improper fractions to mixed numbers calculator - an example

So, let's quickly check how this tool converts improper fractions to mixed numbers. Let's say you have fraction 81/17, and you'd like to find its equivalent as a mixed number:

  1. Enter the numerator of the improper fraction. It's 81.
  2. Input the denominator. 17 in our case.
  3. And that's it - the improper fraction to mixed numbers calculator shows the result:

Improper fraction

Mixed number

⁸¹⁄₁₇

=

4 ¹³⁄₁₇

Could it be more straightforward? 🙂

Hanna Pamuła, PhD
Image: improper fraction to mixed number
Improper fraction
Numerator (n₁)
Denominator (d₁)
Step by step solution?
No
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