Introduction
In this lesson, you will learn how to convert between improper fractions and mixed numbers.
This video illustrates the lesson material below. Watching the video is optional.
Different Fractions
An important part of learning about fractions is becoming comfortable understanding what they mean. Being able to convert between improper fractions and mixed numbers is a great way to understand fractions and recognize how large or small a fraction is. Here are some math terms that will help you to understand this lesson better:
- Proper Fraction: A fraction whose numerator is less than the denominator.
- Example:
- Example:
- Improper Fraction: A fraction whose numerator is greater than the denominator.
- Example:
- Example:
- Mixed Number: An integer combined with a proper fraction showing how many wholes and how many parts are in the number.
- Example:
means 2 wholes and pieces, pronounced "two and one-third."
- Example:
Converting Fractions and Mixed Numbers
Being able to convert between improper fractions and mixed numbers is a great way to be able to understand fractions and recognize how large or small a fraction is.
Example 1
Suppose you went to a party with lots of pizza. At the end, there was some pizza leftover. Below is an image of how much pizza was left over.
Figure 1
If you combine all of the leftover slices, how many pizzas will be left over? These are the fractions you have:
Figure 2
Because all of these fractions have the same denominator (because all of the pizzas had the same amount of slices at the start) you can add the numerators to see how many slices you have leftover.
Now that you know the total of leftover slices is 29, you also know that the fraction of leftover pizza is
To get a better understanding of what
You can combine the
Figure 3
Similarly, you can combine the
Figure 4
Now you can see that there are three full pizzas and
Figure 5
Breaking
Converting a Mixed Number to an Improper Fraction
When converting from a mixed number to an improper fraction:
- Multiply the integer by the denominator
- Add the numerator to get the new numerator.
- Keep the denominator the same.
Example 2
Find the improper fraction of
Example 3
Find the improper fraction of
Another way to look at it:
Example 4
Find the improper fraction of
Because the denominator is 4, you know you are talking about something that has four parts. In this case, that means:
Converting an Improper Fraction to a Mixed Number
When converting from an improper fraction to a mixed number:
- Divide the numerator by the denominator.
- Keep the remainder as the numerator of the new fraction part.
- The denominator stays the same.
Example 5
Figure 6
The mixed fraction is written as
Example 6
Change
To do this, take the numerator, 9, and divide it by the denominator, 4.
Figure 7
9 divided by 4 is 2 with a remainder of 1. The remainder 1 becomes the new numerator. The mixed fraction is written as
Example 7
Change
Figure 8
The mixed fraction is
Things to Remember
- An improper fraction has a numerator that's larger than the denominator.
- A mixed number is an integer combined with a proper fraction showing how many wholes and how many parts are in the number. To convert a mixed number to an improper fraction, take the integer and multiply it by the denominator, and then add the numerator. This becomes the new numerator, and the denominator stays the same.
- To convert an improper fraction to a mixed number, take the numerator and divide it by the denominator.
Practice Problems
Convert the following mixed numbers into improper fractions: (Solution (Video Solution (Solution (Video Solution (Solution (Solution