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Mixed Number to Improper Fraction Calculator

Created by Hanna Pamuła, PhD
Reviewed by Dominik Czernia, PhD and Jack Bowater
Last updated: Jun 05, 2023


Welcome to the mixed number to improper fraction calculator - a tool that can convert fractions in the blink of an eye 😉 If you're wondering how to change a mixed number into an improper fraction, you're in the right place - below, you'll find a short explanation on how to do it by hand. Also, the calculator has a step-by-step guide👣, so don't worry too much about your homework - we'll give you a helping hand when converting mixed numbers to improper fractions!

Check our improper fraction to mixed number calculator if you're on the hunt for the opposite conversion. Additionally, if your number is still a decimal, you can convert it to a mixed number with our mixed number calculator.

How to change a mixed number into an improper fraction?

There are only three steps required when converting mixed numbers to improper fractions. As an example, let's take 2 ⅗ and convert it to an improper fraction:

Step 1

Multiply the whole number by the denominator of the fractional part:

2 × 5 = 10

Step 2

Add the result to your numerator:

10 + 3 = 13

Step 3

The number you just calculated is your new numerator - put it on top of your original denominator:

¹³⁄₅

In this case, the improper fraction is already in its simplest form.

However, it may happen that you need to reduce the fraction. For example, if the result is ²⁸⁄₁₀, you need to calculate the greatest common factor (GCF) and divide both numbers by it:

GCF(28,10) = 2

²⁸⁄₁₀ = ¹⁴⁄₅

Or, even better, you can use our simplify fractions calculator.

Are you still unsure how to change a mixed number into an improper fraction? Let's take a look at a visual example...

Converting mixed numbers to improper fractions - visually 👀

To make it easier to understand and remember, we'll illustrate the conversion of 2 ⅗ again. Let's immerse ourselves into the world of chocolate:

Image explaining how to change a mixed number into an improper fraction. 2 and 3/5 of chocolate bar converted into 13/5 of chocolate bar

In the beginning, you need to find out how many rows are in the whole chocolate bars:

2 whole chocolate bars, each bar has 5 rows:

2 × 5 = 10

Next, add the 3 rows from the incomplete bar:

10 + 3 = 13

Finally, write the number as an improper fraction:

¹³⁄₅

Why do you need to divide by 5 (or, in other words, multiply by ⅕)? Well, that's because each row is a ⅕ of the whole chocolate bar!

So why is converting mixed numbers to improper fractions so useful and important? Imagine you have the chocolate bars from the picture, exactly 2 ⅗ full chocolate bars. You'd like to share your grub with your classmates 🧒🧒🏻🧒🏽. If each person gets one row, how many people can you share it between?

We're sure you guessed that - 13 people! Exactly 13 kids can have one row of chocolate.

Example: convert 3 ¹/₄ to an improper fraction with the mixed number to improper fraction calculator

Using this mixed number to improper fraction calculator is a piece of cake 🍰, but we want to be sure it's crystal clear for you. We'll show you how the tool works on one example: let's say that you'd like to turn 3 ¼ into its improper fraction form:

  1. Input the whole part of the mixed number. In our case, the whole part is equal to 3.
  2. Enter the fractional part. 1 as the numerator and 4 as the denominator.
  3. Sit back and relax😎 - the tool displays the result for you immediately!

Mixed number

Improper fraction

3 ¼

=

¹³⁄₄

  1. If some part of the conversion is still puzzling you, check out the step-by-step solution that we display directly below the mixed number to improper fraction calculator.
Hanna Pamuła, PhD
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Image: mixed number to improper fraction
Whole number (W₁)
Numerator (n₁)
Denominator (d₁)
Step by step solution?
No
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