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

Explanation:

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:
$\frac{\frac{5}{16}}{\frac{3}{2}}$

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

$\frac{\frac{5}{16}}{\frac{3 \cdot 8}{2 \cdot 8}} = \frac{\frac{5}{16}}{\frac{24}{16}}$

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:
$\frac{3}{4} = \frac{\frac{3}{1}}{\frac{4}{1}}$
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 $\frac{5}{24}$, which is quotient of the original expression.