Question

How do you find the quotient of \[\dfrac{5}{16}\] divided by \[\dfrac{3}{2}\]?

Answer 1

Hint: These types of problems, where we are asked to do the division of the fractions have a series of methods to solve. The series is as follows; the first step is to set the expression as a complex fraction. Then, extend the fraction to equal denominators. Finally, solve the expression as a usual fraction. We will look at these steps in detail.

Complete step by step answer:
We are asked to find the quotient of \[\dfrac{5}{16}\] divided by \[\dfrac{3}{2}\]. It means that we have to find the value of \[\dfrac{\dfrac{5}{16}}{\dfrac{3}{2}}\]. Now, let’s look at this fraction. The main numerator consists of a bi-numerator = 5, and a bi-denominator = 16. The main denominator consists of a bi-numerator and bi-denominator as well, they are 3 and 2 respectively.
To work with complex fractions like this, we want to have the same bi-denominator in both parts of the fraction. We have \[\dfrac{\dfrac{5}{16}}{\dfrac{3}{2}}\], here the bi-denominators are 16 and 2. The common multiple of these numbers is 16. So, we want to have both bi-denominators to be 16. This can be done as follows;
 \[\Rightarrow \dfrac{\dfrac{5}{16}}{\dfrac{3\times 8}{2\times 8}}=\dfrac{\dfrac{5}{16}}{\dfrac{24}{16}}\]
As the bi-denominators are the same now, we can just cross them out. So, the above expression becomes, \[\dfrac{5}{24}\].
Hence the quotient is \[\dfrac{5}{24}\].

Note:
 to make this bi-numerator and bi-denominator thing clearer, look at the following example. Let’s say we have a fraction \[\dfrac{3}{4}\]. Then this fraction in bi-numerator and bi-denominator form can also be written as \[\dfrac{3}{4}=\dfrac{\dfrac{3}{1}}{\dfrac{4}{1}}\]. Using this method, we can calculate the division of any two fractions.