Question

Simplify the following:
$11-\left[ \left\{ 7-\left( 5-3\left( 9-3-6 \right) \right) \right\} \right]$

Answer 1

Hint: To simplify the given value we will use the BODMAS Rule. Firstly we always solve a value from the left hand direction starting by simplifying the value in the bracket where first division is done then multiplication is done then addition is done and finally division is done. We will use this rule and get the desired answer.

Complete step by step answer:
We have to simplify the below value:
$11-\left[ \left\{ 7-\left( 5-3\left( 9-3-6 \right) \right) \right\} \right]$
So starting from the right hand side we will solve the round bracket having three values as follows:
$\begin{align}
  & 11-\left[ \left\{ 7-\left( 5-3\left( 9-3-6 \right) \right) \right\} \right] \\
 & \Rightarrow 11-\left[ \left\{ 7-\left( 5-3\left( 6-6 \right) \right) \right\} \right] \\
 & \Rightarrow 11-\left[ \left\{ 7-\left( 5-3\left( 0 \right) \right) \right\} \right] \\
\end{align}$
Now as we open the bracket we get,
$\begin{align}
  & 11-\left[ \left\{ 7-\left( 5-0 \right) \right\} \right] \\
 & \Rightarrow 11-\left[ \left\{ 7-\left( 5 \right) \right\} \right] \\
 & \Rightarrow 11-\left[ 2 \right] \\
 & \Rightarrow 9 \\
\end{align}$
So we got the value as 9.
Hence on simplifying $11-\left[ \left\{ 7-\left( 5-3\left( 9-3-6 \right) \right) \right\} \right]$ we get 9.

Note: An arithmetic expression with multiple operations and brackets are not easy to solve so that BODMAS Rule is used. BODMAS rule is used to solve any value with many operations and brackets in a proper manner so that we get a correct answer. BODMAS is short form or we can say acronym and it stands for Bracket, of, Division, Multiplication, Addition and Subtraction. This rule is used to explain the order in which an expression is solved. It is also necessary that we solve the expression from left to right of the BODMAS Rule. Bracket plays a very significant role in expressions as if their place is changed our solution will change. The operation inside the bracket can be done directly without any rule as it will eventually yield the same answer whether we add or subtract first.