Converting Improper Fractions To Mixed Numbers And Vice Versa

Improper Fractions and Mixed numbers are different ways to represent rational numbers greater than 1. One such example is four and three quarters represented as follows.

4 3/4

This is a rational number that lies between the numbers 4 and 5.  

Rational numbers can always be represented as one integer over another integer. Now, 4 and three quarters is clearly not written in this form; it is a mixed number.

The method by which we convert this mixed number into an improper fraction is as follows:

Multiply the denominator by the integer/whole number.  
4 x 4 = 16

add this value to the numerator.  
16 + 3 = 19

Put our new number back on top of our denominator.  
19/4

So now we have converted our original mixed number into an improper fraction. Now how can we convert improper fractions into mixed numbers.

The number 17/5 is represented as an improper fraction. Remember, 17/5 is the same value as 17 divided by 5. Converting it into a mixed number is as follows.

Divide our denominator into our numerator.  
5 goes into 17 three times with a remainder 2

The three becomes the whole number part of the mixed number. The 2 becomes the numerator of the fractional part.

17/5   =   3  2/5

Notice the numerator stays the same, we effectively split 17/5 into 15/5 (equals 3) and 2/5.