Mixed Fractions
(Also called "Mixed Numbers")
1\frac{3}{4} 
(one and threequarters) 
A Mixed Fraction is a
whole number
and a proper fraction
combined.
Such as 1\frac{3}{4}
Examples
2\frac{3}{8}  7\frac{1}{4}  1\frac{14}{15}  21\frac{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
We can use either an improper fraction or a mixed fraction to show the same amount.
For example 1\frac{3}{4} = \frac{7}{4}, as shown here:
1\frac{3}{4}  \frac{7}{4}  
= 
Converting Improper Fractions to Mixed Fractions
To convert an improper fraction to a mixed fraction, follow these steps:


Example: Convert \frac{11}{4} to a mixed fraction.
Divide:
Write down the 2 and then write down the remainder (3) above the denominator (4).
Answer:
2 \frac{3}{4}
That example can be written like this:
Example: Convert \frac{10}{3} to a mixed fraction.
Answer:
3 \frac{1}{3}
Converting Mixed Fractions to Improper Fractions
To convert a mixed fraction to an improper fraction, follow these steps:


Example: Convert 3\frac{2}{5} to an improper fraction.
Multiply the whole number part by the denominator:
Add that to the numerator:
Then write that result above the denominator:
\frac{17}{5}
We can do the numerator in one go:
Example: Convert 2\frac{1}{9} 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?
Mixed Fraction:  What is:  1 + 2\frac{1}{4}  ?  

Is it:  1 + 2 + \frac{1}{4}  = 3\frac{1}{4} ?  
Or is it:  1 + 2 × \frac{1}{4}  = 1\frac{1}{2} ?  
Improper Fraction:  What is:  1 + \frac{9}{4}  ?  
It is:  \frac{4}{4} + \frac{9}{4} = \frac{13}{4} 
But, for everyday use, people understand mixed fractions better.
Example: It is easier to say "I ate 2\frac{1}{4} sausages", than "I ate \frac{9}{4} sausages"
We Recommend:
 For Mathematics: Improper Fractions
 For Everyday Use: Mixed Fractions