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Introduction

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Introduction

Improper Fractions and Mixed Numbers

To help us better understand mixed numbers and improper fractions, we like to imagine them as pizzas or legos.

Pick whichever you vibe with more:

INTRO
A mixed number tells us how many whole numbers and parts we have, and an improper fraction tells us how many total parts we have when the parts make up at least one whole.
We can use an improper fraction and a mixed number to represent the same thing. For example, we can either say we have 2 whole pizzas and 3 slices of pizza, where 4 slices make up a whole:
Or we can say we have slices of pizza where 4 slices make up a whole:
They're just two ways of saying the same thing 👯.
Check out our
Calculator
or explore our
Lesson
and
Practice
sections to learn more about improper fractions and mixed numbers and test your understanding.

You can also use the Quick Links menu on the left to jump to a section of your choice.

You can also use the Quick Links dropdown above to jump to a section of your choice.

CALCULATOR

Improper Fraction to Mixed Number Calculator

Mixed Number to Improper Fraction Calculator

Convert a

Step 1. Explain the fraction.

For now, ignore the negative sign.


In pizza terms, for example, means there are total slices where slices make up a whole pizza.

Step 2. Set up the conversion.

We want to split up our fraction into a whole number and the leftover fraction:
In pizza terms, this is like figuring out how many whole pizzas and leftover slices there are:


Step 3. Find the whole number.

This is equal to the number of times the denominator goes into the numerator and tells us how many whole numbers we can make from the total number of equal parts we have.


In pizza terms, since goes into times, we can make whole pizzas.

Step 4. Find the leftover/remainder.

Each of the whole pizzas has slices. So that’s slices used, which means we have slices leftover.


Step 5. Drop the plus sign.

Since the top of the fraction is , the fraction simplifies to .
So, our answer is .
KEY STEPS

How to Convert from Improper Fractions to Mixed Numbers

How to Convert from Mixed Numbers to Improper Fractions

Convert a

Step 1. Explain the fraction.



In pizza terms, for example, means there are total slices where slices make up a whole pizza.

Step 2. Set up the conversion.

We want to split up our fraction into a whole number and the leftover fraction:
In pizza terms, this is like figuring out how many whole pizzas and leftover slices there are:


Step 3. Find the whole number.

This is equal to the number of times the denominator goes into the numerator and tells us how many whole numbers we can make from the total number of equal parts we have.
In pizza terms, we're figuring out how many whole pizzas we can make:


Step 4. Find the leftover/remainder.

In pizza terms, this is like finding the leftover slices after forming our whole pizzas:
Ex:


Step 5. Drop the plus sign.

Ex:

Step 1. Add the plus sign.

Add in the hidden plus sign between the whole number and fraction.
Ex: .

Step 2. Explain the mixed number.



In pizza terms, for example, means there are 2 whole pizzas and 1 slice leftover, where 4 slices make up a whole pizza.

Step 3. Set up the conversion

We want to combine our whole number and fraction so that we can easily see the total number of equal parts we have.
In pizza terms, this is like finding the total number of equal slices there are:


Step 4. Find the new numerator.

We need to figure out how many equal sized parts are in the whole numbers and add them to the leftover parts:
In pizza terms, this is like combining the number of slices in the whole pizzas with the number of leftover slices:


LESSON
Converting Improper Fractions to Mixed Numbers

Converting Improper Fractions to Mixed Numbers

An improper fraction is a fraction where the numerator is greater than or equal to the denominator. It tells us how many equal-sized parts there are and how big the parts are.



To convert an improper fraction into a mixed number, we have to figure out how many wholes can be created from the parts, and then how many leftover parts are left.
So, if we have slices where slices make up a whole pizza, then we can make whole pizza, with slices leftover:

Improper Fraction

Mixed Number

Let's try some examples!

EXAMPLE 1

Let's start by converting this improper fraction to a mixed number:

Step 1. Explain the fraction.

For now, ignore the negative sign.


In pizza terms, for example, means there are total slices where slices make up a whole pizza.

Step 2. Set up the conversion.

We want to split up our fraction into a whole number and the leftover fraction:
In pizza terms, this is like figuring out how many whole pizzas and leftover slices there are:


Step 3. Find the whole number.

This is equal to the number of times the denominator goes into the numerator and tells us how many whole numbers we can make from the total number of equal parts we have.


In pizza terms, since goes into times, we can make whole pizzas.

Step 4. Find the leftover/remainder.

Each of the whole pizzas has slices. So that’s slices used, which means we have slices leftover.


Step 5. Drop the plus sign.

Since the top of the fraction is , the fraction simplifies to .
So, our answer is .

EXAMPLE 2

Nice work! Now try converting this improper fraction to a mixed number:

Step 1. Explain the fraction.

For now, ignore the negative sign.


In pizza terms, for example, means there are total slices where slices make up a whole pizza.

Step 2. Set up the conversion.

We want to split up our fraction into a whole number and the leftover fraction:
In pizza terms, this is like figuring out how many whole pizzas and leftover slices there are:


Step 3. Find the whole number.

This is equal to the number of times the denominator goes into the numerator and tells us how many whole numbers we can make from the total number of equal parts we have.


In pizza terms, since goes into times, we can make whole pizzas.

Step 4. Find the leftover/remainder.

Each of the whole pizzas has slices. So that’s slices used, which means we have slices leftover.


Step 5. Drop the plus sign.

Since the top of the fraction is , the fraction simplifies to .
So, our answer is .
Awesome! Expand the
Practice
below to try some more problems or expand the next
Lesson
to explore what we do when we're converting mixed numbers to improper fractions.
PRACTICE
Converting Improper Fractions to Mixed Numbers

Practice: Converting Improper Fractions to Mixed Numbers

Question 1 of 10: Convert into a mixed number.

Step 1. Explain the fraction.



In pizza terms, for example, means there are total slices where slices make up a whole pizza.

Step 2. Set up the conversion.

We want to split up our fraction into a whole number and the leftover fraction:
In pizza terms, this is like figuring out how many whole pizzas and leftover slices there are:


Step 3. Find the whole number.

This is equal to the number of times the denominator goes into the numerator and tells us how many whole numbers we can make from the total number of equal parts we have.
In pizza terms, it's how many whole pizzas we can make with slices if one pizza is made of slices.


Step 4. Find the leftover/remainder.

Nice work! Now plug the leftovers in:


Step 5. Drop the plus sign.



Great work! Our answer is

LESSON
Converting Mixed Numbers to Improper Fractions

Converting Mixed Numbers to Improper Fractions

A mixed number is a combination of a whole number and a fraction. It tells us how many whole numbers there are and many leftover parts there are.



To convert a mixed number into an improper fraction, we have to figure out how many parts are in the wholes, and then add that to the leftover parts to get the total number of equal-sized parts.
If we have whole pizzas where slices make up a whole pizza, then we have slices. Adding that to the slices leftover, we have a total of slices:

Mixed Number

Improper Fraction

Let's try some examples!

EXAMPLE 1

Let's start by converting this mixed number to an improper fraction:

Step 1. Add the plus sign.

Add in the hidden plus sign between the whole number and fraction.
And for now, put the negative sign on the outside and ignore it.

Step 2. Explain the mixed number.



In pizza terms, for example, means there are 3 whole pizzas and 2 slices leftover, where 5 slices make up a whole pizza.

Step 3. Set up the conversion

We want to combine our whole number and fraction so that we can easily see the total number of equal parts we have.
In pizza terms, this is like finding the total number of equal slices there are:

Step 4. Find the new numerator.

We need to figure out how many equal sized parts are in the whole numbers and add them to the leftover parts:
So, when we count up all the slices from both the whole pizzas and leftovers, we have total slices all of equal size:
So, our answer is .

EXAMPLE 2

Amazing! Now, let's convert this mixed number to an improper fraction:

Step 1. Add the plus sign.

Add in the hidden plus sign between the whole number and fraction.
And for now, put the negative sign on the outside and ignore it.

Step 2. Explain the mixed number.



In pizza terms, for example, means there are 4 whole pizzas and 1 slices leftover, where 3 slices make up a whole pizza.

Step 3. Set up the conversion

We want to combine our whole number and fraction so that we can easily see the total number of equal parts we have.
In pizza terms, this is like finding the total number of equal slices there are:

Step 4. Find the new numerator.

We need to figure out how many equal sized parts are in the whole numbers and add them to the leftover parts:
So, when we count up all the slices from both the whole pizzas and leftovers, we have total slices all of equal size:
So, our answer is .
Awesome! If you’d like to practice additional problems converting mixed numbers to improper fractions, expand the
Practice
below before closing out this lesson! ⚡
PRACTICE
Converting Mixed Numbers to Improper Fractions

Practice: Converting Mixed Numbers to Improper Fractions

Question 1 of 10: Convert into an improper fraction.

Step 1. Add the plus sign.

Add in the hidden plus sign between the whole number and fraction.

Step 2. Explain the mixed number.



In pizza terms, means there are whole pizzas and slices leftover, where slices make up a whole pizza.

Step 3. Set up the conversion

We want to combine our whole number and fraction so that we can easily see the total number of equal parts we have.
In pizza terms, this is like finding the total number of equal slices there are. What is our denominator?


Step 4. Find the new numerator.

We need to figure out how many equal sized parts are in the whole numbers and add them to the leftover parts:
Nice work! Now plug the new numerator and denominator in:


Great work! Our answer is

CONCLUSION
Incredible job, look at you go! Thanks for checking out this lesson ☺️🙏. Where to next?