Question

How do you simplify the fraction $\dfrac{9}{24}$ ?

Answer 1

Hint: To simplify the fraction given in the above problem i.e. $\dfrac{9}{24}$, we will first see whether the numerator and the denominator is dividing by the same number. If yes, then we will divide the numerator and the denominator by the same number and will write the simpler version of the fraction given above. Similarly, after dividing the numerator and the denominator by the same number, we will again see if the numerator and the denominator that we got is still divisible or not. We will do such division till the numerator and denominator has no common factor other than 1.

Complete step by step answer:
The fraction given above that we have to simplify is as follows:
$\dfrac{9}{24}$
As you can carefully see the numerator and the denominator of the above fraction you will find that 3 is a factor which is common in both the numerator and denominator. To verify that we are going to write the prime factorization of numerator and the denominator as follows:
Prime factorization for 9:
$9=3\times 3\times 1$
Prime factorization of 24:
$24=3\times 2\times 2\times 2\times 1$
Now, writing this prime factorization in the numerator and the denominator we get,
$\dfrac{3\times 3\times 1}{3\times 2\times 2\times 2\times 1}$
From the above fraction you can see that the factor $3\times 1$ will be cancelled out from the numerator and the denominator and we are left with:
$\begin{align}
  & \dfrac{3}{2\times 2\times 2} \\
 & =\dfrac{3}{8} \\
\end{align}$
Now, as you can see that there is no common factor in numerator and denominator so we have simplified the given fraction into $\dfrac{3}{8}$.

Note: You can even divide the numerator by denominator of the simplified version of the fraction given above in the following way:
$8\overset{0.375}{\overline{\left){\begin{align}
  & 30 \\
 & 24 \\
 & \overline{\begin{align}
  & 060 \\
 & 056 \\
 & \overline{\begin{align}
  & 0040 \\
 & \dfrac{0040}{0000} \\
\end{align}} \\
\end{align}} \\
\end{align}}\right.}}$
From the above division, we have got the quotient as 0.375.
So, in the multiple choice questions you might find an option in which only a fraction is given which we have solved in the above solution. And in some questions, you might see an option in which decimal is given which is 0.375.