How do you find the quotient of 5/16 divided by 3/2?

1 Answer
Nov 9, 2015


  • Set the expression up as a complex fraciton
  • Extend the fraction to equal denominators
  • Solve like an usual fraction


First of all, let's look at the parts of our fraction. The main numerator consists of a bi-numerator = 5, and a bi-denomiator = 16.
The main denominator consists of a bi-numerator and bi-denominator as well (3 and 2).

To work with complex fractions like this, we want to have the same bi-denominator in both parts of the fraction.

What we have is:

The smallest common bi-denomiator is 16, so let's expand the main denomiator by 8:

#(5/16)/((3*8)/(2*8)) = (5/16)/(24/16)#

Since the bi-denomiators are the same, we can just cross them out. If this doesn't make any sense, have a look at this:
#3/4 = (3/1) / (4/1)#
NOTE: the expression above has nothing to do with the original expression, I'm just explaining why we can cross out the bi-denominators.

After we have crossed out the common bi-denominators, we are left with #5/24#, which is quotient of the original expression.