Question

How do you write the answer \[\dfrac{3}{16}\times \dfrac{4}{9}\] in the simplest form.

Answer 1

Hint: The given problem is based on fractions. A fraction is a number that is expressed as one number over another number. The number at the top of the fraction is called the numerator and the number on the bottom is the denominator. There are three types of fraction, they are a proper fraction, an improper fraction, and a mixed fraction. The fraction is in the simplest form when the numerator/denominator has only 1 as a common factor. Here in this problem, we are going to simplify the proper fractions and multiply it.

Complete step by step answer:
We know that the given proper fraction is of the form,
\[\dfrac{3}{16}\times \dfrac{4}{9}\]…….. (1)
Here in the fraction \[\dfrac{3}{16}\],we can write the denominator 16 as \[4\times 4\]
Here in the fraction \[\dfrac{4}{9}\], we can write the denominator 9 as \[3\times 3\]
We can write the equation (1) as,
\[\Rightarrow \dfrac{3}{4\times 4}\times \dfrac{4}{3\times 3}\]
In the above fractions, we canceled the identical numbers to get the simplest form.
Now, we get
\[\Rightarrow \dfrac{1}{4}\times \dfrac{1}{3}\]
Now, we can multiply the above fraction, we get
\[\Rightarrow \dfrac{1}{12}\]
Therefore, the simplest form of the fraction \[\dfrac{3}{16}\times \dfrac{4}{9}\] is \[\dfrac{1}{12}\].

Note:
Here students may make mistakes while canceling the terms, students have to remember the multiplication tables so that it is easy to solve and simplify these fraction type problems. Here in this problem, we have to understand the concept, that is the fraction is in the simplest form when the numerator/denominator has only 1 as a common factor.