Dividing Fractions
Objective Learn the procedure for dividing
one fraction by another.
There is a main difference between the division of whole
numbers and the division of fractions. In fact, when one whole
number is divided by another, there may be a remainder since one
whole number cannot always be divided evenly into another whole
number. However, there is never a remainder when two fractions
are divided; the result is always another fraction or a whole
number.
When dividing by a fraction we need to invert the fraction and
change the division symbol to multiplication. Then we complete
the multiplication using the skills.
Example 1
What is the value of ?
Solution
Change from dividing by to multiplying by its reciprocal, . Then multiply.
Example 2
Find .
Solution


Change to multiplication by the
reciprocal. 


Write the improper fraction as a mixed
number. 
The same procedure works when dividing one fraction by another
fraction.
Key Idea
To divide one fraction (the dividend) by another (the
divisor), multiply the dividend by the reciprocal of the divisor.
In symbols, .
Example 3
What is the value of ?
Solution


Multiply by the reciprocal of the
divisor. 


Multiply numerators and denominators
separately. 


Write the improper fraction as a mixed number. 
Example 4
Find .
Solution


Multiply by the reciprocal of the
divisor. 


Multiply numerators and denominators
separately. 



