Mixed fractions and Improper Fractions

In this lesson we will focus on fractions that are actually greater than one. I've always known them as Mixed Numbers, but I've found that many people are calling them mixed fractions. Depending on how the number is written is may also be an improper fraction.

So, after all the talk about proper fractions, and how a fraction is "part of a whole" or less than 1, how we can we now say that some fractions are actually greater than 1?


If we have a whole plus part of a whole, then we actually have a mixed number. It's easier explained through a graphic. Take a look....



Mixed Numbers



Writing Fractions that are Greater than One

Our Mixed Number of One and one-half above, can be written two ways. Take a look...

mixed fractions

In many cases, an improper fraction is easier to work with than a mixed number. Therefore, mixed numbers are often converted to improper fractions. How do we do this?

Converting a Mixed Number to an Improper Fraction

MIxed number example

improper fraction example


So, now you know the rules for converting a mixed number to an improper fractions are:

Rules for Converting a Mixed Number to an Improper Fraction

1. Multiply the denominator times the whole number and then add the numerator. This is the new numerator.

2. Write this number over the existing denominator.

3. This is your new improper fraction.

Just to make sure you completely understand, let's take a look at one more example.

Example 1 - Rewriting Mixed Numbers as Improper Fractions

writing improper fractons




So, if we can rewrite a mixed number as an improper fraction, then we surely must be able to write an improper fraction as a mixed number!

Converting an Improper Fraction to a Mixed Number

writing mixed numbers

We'll take a look at one more example, just to make sure you can convert an improper fraction to a mixed fraction.


Rewriting an Improper Fraction as a Mixed Number - Example 2

mixed numbers

Hopefully now you understand the difference between an improper fraction and a mixed fraction. You should also be able to convert from one to the other.


More Pre-Algebra Fraction Lessons



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