How to make a mixed fraction into an improper fraction

Mixed numbers are a combination of a whole number and proper fractions. Here’s an example:

Mixed numbers show a value somewhere between two whole numbers. For example, the mixed number above is neither 1 nor 2. The one-half fraction shows it's perfectly in between.

Let's dive further into what mixed numbers are and how they can be converted into another type of fraction, improper fractions.

What Are Mixed Numbers?

Mixed numbers, which are also called mixed fractions, have a whole number part and a fraction part.

The fraction part must be a proper fraction, which means that the numerator (the top number) is smaller than the denominator (the bottom number).

Now that we've defined mixed numbers, let's learn how to convert them into improper fractions.

What Are Improper Fractions?

An improper fraction has a numerator with a larger value than the denominator:

Because the denominator is a larger value, the decimal quotient will always be greater than one:

Converting Mixed Numbers Into Improper Fractions

Let's learn how to go from the mixed number form to the improper fraction form following these steps:

1. Multiply the whole number by the denominator:

1. Add the resulting number to the numerator:

1. Place this number over the original denominator:

Understanding Mixed Numbers and Improper Fractions

Mixed numbers are a combination of whole numbers and proper fractions. Improper fractions have a larger numerator than denominator.

Learning how to convert a mixed number into an improper fraction prepares you for the next lesson you'll probably have to learn in math: converting improper fractions into mixed numbers.

More Math Homework Help

• Negative Number Line: What It Is and How To Use It
• A Step-by-Step Guide to Dividing Fractions With Whole Numbers
• How to Write a Fraction as a Decimal: 2 Simple Methods

An Improper Fraction has a top number larger than (or equal to) the bottom number.

It is usually "top-heavy"

More Examples

See how the top number is bigger than (or equal to) the bottom number?
That makes it an Improper Fraction, (but there is nothing wrong about Improper Fractions).

Three Types of Fractions

There are three types of fraction:

Fractions

A Fraction (such as 7/4) has two numbers:

NumeratorDenominator

The top number (the Numerator) is the number of parts we have.
The bottom number (the Denominator) is the number of parts the whole is divided into.

Example: 7/4 means:

• We have 7 parts
• Each part is a quarter (1/4) of a whole
  

So we can define the three types of fractions like this:

Improper Fraction

So an improper fraction is a fraction where the top number (numerator) is greater than or equal to the bottom number (denominator): it is top-heavy.

Can be Equal

What about when the numerator is equal to the denominator? For example 4/4 ?

Well it is the same as a whole, but it is written as a fraction, so most people agree it is a type of improper fraction.

Improper Fractions or Mixed Fractions

We can use either an improper fraction or a mixed fraction to show the same amount.

For example 134 = 74, as shown here:

Converting Improper Fractions to Mixed Fractions

To convert an improper fraction to a mixed fraction, follow these steps:

	Divide the numerator by the denominator. Write down the whole number answer Then write down any remainder above the denominator.

Example: Convert 114 to a mixed fraction.

Divide:

11 ÷ 4 = 2 with a remainder of 3

Write down the 2 and then write down the remainder (3) above the denominator (4).

Answer:

2 34

That example can be written like this:

Example: Convert 103 to a mixed fraction.

Answer:

3 13

Converting Mixed Fractions to Improper Fractions

To convert a mixed fraction to an improper fraction, follow these steps:

	Multiply the whole number part by the fraction's denominator. Add that to the numerator Then write the result on top of the denominator.

Example: Convert 325 to an improper fraction.

Multiply the whole number part by the denominator:

3 × 5 = 15

Add that to the numerator:

15 + 2 = 17

Then write that result above the denominator:

175

We can do the numerator in one go:

Example: Convert 219 to an improper fraction.

Are Improper Fractions Bad ?

NO, they aren't bad!

For mathematics they are actually better than mixed fractions. Because mixed fractions can be confusing when we write them in a formula: should the two parts be added or multiplied?

But, for everyday use, people understand mixed fractions better.

Example: It is easier to say "I ate 214 sausages", than "I ate 94 sausages"

We Recommend:

• For Mathematics: Improper Fractions
• For Everyday Use: Mixed Fractions