Question

Simplify the expression $36-\left[ 18-\left\{ 14-\left( 15-4\div 2\times 2 \right) \right\} \right]$.

Answer 1

Hint: For this type of question, we cannot directly solve from left to right or right to left. There is a particular order which we have to follow. The priority order for the operations is given by the BODMAS rule. The BODMAS priority order says that we have to solve the brackets first, then order, division, multiplication, addition, and subtraction. Solve it according to this and evaluate.

Complete step by step solution:
The given expression is, $36-\left[ 18-\left\{ 14-\left( 15-4\div 2\times 2 \right) \right\} \right]$
To solve this expression, we use the BODMAS rule.
This BODMAS rule says the priority order of the arithmetic operations to be performed while solving an expression.
The postulate’s priority order is,
B - Brackets
O - Order
D - Division
M - Multiplication
A - Addition
S – Subtraction.
Now let us start solving the expression.
$\Rightarrow 36-\left[ 18-\left\{ 14-\left( 15-4\div 2\times 2 \right) \right\} \right]$
The first position in the priority order is brackets.
Hence, we solve the innermost brackets first.
In the innermost brackets also, we solve the division first since it has the highest priority compared to division and multiplication.
$\Rightarrow 36-\left[ 18-\left\{ 14-\left( 15-2\times 2 \right) \right\} \right]$
Now in between subtraction and multiplication, multiplication has the higher precedence.
$\Rightarrow 36-\left[ 18-\left\{ 14-\left( 15-4 \right) \right\} \right]$
Now solve the innermost brackets.
$\Rightarrow 36-\left[ 18-\left\{ 14-11 \right\} \right]$
Again, solve the innermost bracket, the parenthesis.
$\Rightarrow 36-\left[ 18-3 \right]$
On further evaluating we get,
$\Rightarrow 36-15$
$\Rightarrow 21$
Hence, the expression, $36-\left[ 18-\left\{ 14-\left( 15-4\div 2\times 2 \right) \right\} \right]$ upon simplification results to 21.

Note: The BODMAS rule explains the order of operations which will be performed while solving an expression. The “O” in BODMAS means order and that means that we need to solve for powers and roots as the second priority. The “B” in BODMAS means brackets. There is a particular order for the type of brackets too. The () bracket has a higher priority than {} and then the bracket with the least priority is the [] bracket.