Question

The value of $8\times 2\times 96\div \left( 12\times 4 \right)$ is
(a) 12
(b) 32
(c) 48
(d) 24

Answer 1

Hint: To find the value of $8\times 2\times 96\div \left( 12\times 4 \right)$ , we have to use the BODMAS rule. BODMAS stands for Bracket, Order, Division, Multiplication, Addition, and Subtraction. We have to simplify an expression in the order of the letters in the BODMAS. So firstly, we have to simplify the terms inside the bracket. Then, we have to divide this result with 96 and simplify.

Complete step by step answer:
We have to find the value of $8\times 2\times 96\div \left( 12\times 4 \right)$ . We will use the BODMAS rule to simplify the expression. BODMAS stands for Bracket, Order, Division, Multiplication, Addition, and Subtraction. We have to simplify an expression in the order of the letters in the BODMAS. So firstly, we have to simplify the terms inside the bracket. Let us multiply 12 with 4.
$\begin{align}
  & \Rightarrow 8\times 2\times 96\div \left( 12\times 4 \right) \\
 & \Rightarrow 8\times 2\times 96\div 48 \\
\end{align}$
In BODMAS, the next priority comes to division. So let us divide 96 by 48.
$\begin{align}
  & \Rightarrow 8\times 2\times \dfrac{96}{48} \\
 & =8\times 2\times 2 \\
\end{align}$
Now, we have to multiply the terms. We will get the result of this step as
$\Rightarrow 8\times 2\times 96\div \left( 12\times 4 \right)=32$

So, the correct answer is “Option b”.

Note: Students must understand the BODMAS rule thoroughly and use it to simplify expressions containing multiple operations. If the BODMAS rule is not followed, the answer turns out to be wrong. BODMAS rule is also known as PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction). We can directly write
$8\times 2\times 96\div \left( 12\times 4 \right)$ as
$\Rightarrow 8\times 2\times \dfrac{96}{\left( 12\times 4 \right)}$
Now, we can simplify the above expression by cancelling the common factors.
\[\Rightarrow {{\require{cancel}\cancel{8}}^{2}}\times 2\times \dfrac{96}{12\times \require{cancel}\cancel{4}}\]
We can write the result of this step as
\[\Rightarrow 2\times 2\times \dfrac{96}{12}\]
Let us again cancel the common factors.
\[\begin{align}
  & \Rightarrow \require{cancel}\cancel{2}\times 2\times \dfrac{96}{{{\require{cancel}\cancel{12}}^{6}}} \\
 & =2\times \dfrac{96}{6} \\
\end{align}\]
We can strike out the common factor 2.
\[\begin{align}
  & \Rightarrow \require{cancel}\cancel{2}\times \dfrac{96}{{{\require{cancel}\cancel{6}}^{3}}} \\
 & =\dfrac{96}{3} \\
\end{align}\]
Let us divide 96 by 3.
$\Rightarrow \dfrac{96}{3}=32$