Mixed Fractions
(Also called "Mixed Numbers")
A Mixed Fraction 

1 ^{3}/_{4}  
(one and threequarters) 
Examples
2 ^{3}/_{8}  7 ^{1}/_{4}  1 ^{14}/_{15}  21 ^{4}/_{5} 
See how each example is made up of a whole number and a proper fraction together? That is why it is called a "mixed" fraction (or mixed number).
Names
We can give names to every part of a mixed fraction:
Three Types of Fractions
There are three types of fraction:
Mixed Fractions or Improper Fractions
You can use either an improper fraction or a mixed fraction to show the same amount.
For example 1 ^{3}/_{4} = ^{7}/_{4}, as shown here:
1 ^{3}/_{4}  ^{7}/_{4}  
= 
Converting Mixed Fractions to Improper Fractions
To convert a mixed fraction to an improper fraction, follow these steps:

Example: Convert 3 ^{2}/_{5} to an improper fraction.
Multiply the whole number by the denominator:
Add the numerator to that:
Then write that down above the denominator, like this:
17 
5 
Converting Improper Fractions to Mixed Fractions
To convert an improper fraction to a mixed fraction, follow these steps:

Example: Convert 11/4 to a mixed fraction.
Divide:
Write down the 2 and then write down the remainder (3) above the denominator (4), like this:
2  3 
4 
When to Use Improper Fractions or Mixed Fractions
For everyday use, people understand mixed fractions better:
Example: It is easier to say "I ate 2 ^{1}/_{4} sausages", than "I ate ^{9}/_{4} sausages"
But for mathematics improper fractions are actually better than mixed fractions.
Because mixed fractions can be confusing when you write them down in a formula (are the two parts supposed to be added or multipled?):
Mixed Fraction:  What is:  1 + 2 ^{1}/_{4}  ?  

Is it:  1 + 2 + ^{1}/_{4}  = 3 ^{1}/_{4} ?  
Or is it:  1 + 2 × ^{1}/_{4}  = 1 ^{1}/_{2} ?  
Improper Fraction:  What is:  1 + ^{9}/_{4}  ?  
It is:  ^{4}/_{4} + ^{9}/_{4} = ^{13}/_{4} 
We Recommend:
 For Mathematics: Improper Fractions
 For Everyday Use: Mixed Fractions