Dividing Fractions:

Remember that given a fraction, such as , the top number is the numerator (namely 1) and the bottom number is the denominator (namely 2) 

Recall that the reciprocal of a fraction is the multiplicative inverse and is produced by inverting the fraction (placing the original numerator as the denominator and the original denominator as the numerator)For example, the reciprocal of is

Example 1:

Whenever you divide fractions, first you find the reciprocal of the second fraction (divisor) then you multiply the numerators to create the answer numerator, and multiply the denominators to create the answer denominator.

 

Example 2:

Whenever you divide fractions, first you find the reciprocal of the second fraction (divisor) then you multiply the numerators to create the answer numerator, and multiply the denominators to create the answer denominator.Since we are not doing cross-cancellation in this particular instance, you must also reduce your final fraction.

 

Donít forget to reduce your answer to lowest terms, i.e.

 

We will do an example that utilizes cross-cancellation.

Example 3:

Lets first find the reciprocal of the second fraction (divisior)

Instead of multiplying first, we can combine the factors of the numerator and denominator and make one fraction that is equivalent to the original problem.This is called cross-canceling:(The 5 and the 10 in both the numerator and denominator respectively can be reduced from to and the 3 and the 6 in numerator and denominator respectively can be reduced from to ) You may cancel any common factors from the numerator and denominator as shown in the following example:

The method shown in example 3 is the preferred method, but if you are uncomfortable, use the method in example 2 for a while until you get the hang of it, then try the method in example 3 and compare the answers you get.

 

Try this problem using the method of your choice:

 


 

 

When you are ready, click here to go to the division of fractions with unlike denominators practice page.  You may need some scratch paper to do the practice.