Improper Fraction To Mixed Number
w/ 21+ Examples!

How to turn an improper fraction to a mixed number?

Jenn, Founder Calcworkshop^®, 15+ Years Experience (Licensed & Certified Teacher)

Great question!

Because that’s what we’re covering today with 22 step-by-step examples!

Let’s go!

Math Fractions

But first, let’s remind ourselves about fractions.

A fraction tells us how items are divided, and we think of fractions as the part over the whole.

Part To Whole — Definition

The numerator, which is the number on the top, indicates the part being counted. And the denominator, which is the number on the bottom, shows the total parts as a whole.

This means that depending on what we are counting, or what we want to show, our numerator may change.

Visual Example

For instance, look at the following image. The fractions are different depending on whether we want to count the shaded region or the non-shaded region.

Visualizing Fractions

Fraction Vocabulary

There are three major types of fractions: proper fractions, improper fractions, mixed fractions. And it’s important to know the similarities and differences between each classification, so we can easily transform fractions from one type to another.

Let’s look at each type more closely.

Proper Fraction Definition

Numerator Smaller Than Denominator

Now, I’m sure you noticed that we have absolute value bars surrounding the n and d values.

Do we need them?

Well, eventually we will be working with both positive and negative numbers (yes, great things to come!), for now, just know that a proper fraction means the numerator is smaller than the denominator, and you can ignore the absolute value.

What Is An Improper Fraction

But as you know, not all fractions are proper, as you can see in the following instance.

Improper Fraction — Definition

This picture shows that the denominator divides the numerator at least one time — resulting in an improper fraction.

Numerator Greater Than Denominator

And once again, while we are currently only considering positive numbers at this point in our study, please know that eventually, we will be dealing with negative numbers too, so that’s why we see the absolute value symbols.

But don’t worry, the process and concept are the same. If the numerator is bigger than or equal to the denominator, it’s an improper fraction.

What Is A Mixed Number

Now it’s time to see how improper fractions are related to mixed numbers.

Using the problem above, notice that we could have easily said 5/4 is the same as 1 and 1/4.

In fact, a whole number or mixed number is considered the simplest form of an improper fraction.

Moreover, this means that the improper fraction is equivalent to the mixed number, and visa-versa, as they have the same value as discussed on Splash Learn.

And being able to go back and forth between a mixed number and an improper fraction is an essential skill.

Why?

Because you will often find, as you get to Algebra and other higher-level math courses, that it is easier to work with improper fractions rather than mixed numbers, so mastering this skill now is extremely important.

How To Turn An Improper Fraction Into A Mixed Number

So, how do you convert a fraction into its equivalent mixed number or whole number?

Steps

1. First, divide the numerator by the denominator using long division, to identify our quotient and remainder.
2. Second, place the remainder over the denominator and add it to our quotient.

How To Convert an Improper Fraction To a Mixed Number

Solved Example

For this question, let’s rewrite the fraction 11/5 as a mixed number.

Improper Fraction To Mixed Number — Example

This shows us that 11/5 is equivalent to 2 and 1/5.

How To Change A Mixed Number Into An Improper Fraction

Okay, so now let’s go the other way and convert mixed numbers into improper fractions.

Steps

1. First, take the denominator and multiply it by the whole number.
2. Second, add the numerator to the product.

In other words, we multiply and add!

How To Convert a Mixed Number Into an Improper Fraction

Worked Example

For instance, let’s rewrite the mixed number 3 and 1/4 as an improper fraction.

Mixed Number To Improper Fraction — Example

This means that 3 and 1/4 are equivalent to 13/4.

Equivalent Fractions

What’s important to note is that equivalent fractions have different numerators and possibly different denominators, but they represent the same value or proportion of the whole.

Equivalent Fractions — Definition

Let’s look at a few examples of some equivalent fractions.

Detailed Example

Suppose we are given the fraction 5/9 and we want to transform this fraction so that we have a new denominator of 18. How do we do this?

Multiply To Find Equivalent Fractions — Example

Worked Example

Suppose we are given the fraction 16/24 and wish to simplify or reduce this fraction so that our denominator is the value of 3. What do we do?

Equivalent Fractions Division — Example

And that’s it!

Using countless problems, we will look at:

• Whole Number Fractions
• Mixed Number Fractions
• Improper Fraction
• Equivalent Fractions

And learn how to convert between the improper and mixed number with ease.

Worksheet (PDF) — Hands on Practice

Put that pencil to paper in these easy to follow worksheets — expand your knowledge!

Improper Fraction To Mixed Number — Practice Problems
Improper Fraction To Mixed Number — Step-by-Step Solutions

Let’s do it!

Video Tutorial — Full Lesson w/ Detailed Examples

46 min

• Introduction to Video: Improper Fractions and Mixed Numbers
• 00:00:27 – What is a proper fraction, improper fraction, mixed number and whole number?

• 00:10:00 – How do you write a fraction as a mixed number?
• 00:12:51 – Change fractions to mixed or whole numbers (Examples #1-6)
• 00:22:37 – How do you write a mixed number as an improper fractions? (Examples #7-14)
• 00:31:03 – Finding equivalent whole numbers and fractions (Examples #15-19)
• 00:40:06 – Find the equivalent fraction (Examples #20-22)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions