Question

Simplify the following expression: $45 - [38 - \{ 60 \div 3 - (6 - 9 \div 3) \div 3\} ]$

Answer 1

Hint: According to given in the question we have to simplify the value of the expression $45 - [38 - \{ 60 \div 3 - (6 - 9 \div 3) \div 3\} ]$, so to solve the expression first of all we have to follow the BODMAS rule as explained below:
B – Brackets of (according to this first of all we have solve the smaller bracket then we have to solve curly bracket and after it we have to solve large bracket)
O- Order
D – Divide
M – Multiply
A – Subtract
A – Addition
Hence, with the help of the BODMAS rule as explained above first of all we have to solve the terms inside the smaller bracket and in the smaller bracket first of all we will divide and then subtract the terms inside the smaller bracket. Now we will solve the value inside the curly bracket so first we will divide and then subtract and after it we have to solve all the terms inside the large bracket to find the value of the given expression.

Complete step by step answer:
Step 1: First of all we have to solve the smaller bracket of the given expression in which first we will divide the terms and then subtract.
$
   = 45 - [38 - \{ 60 \div 3 - (6 - 3) \div 3\} ] \\
   = 45 - [38 - \{ 60 \div 3 - (3) \div 3\} ] \\
 $
Step 2: Now, we have to solve the curly bracket of the given expression in which first we will divide the terms and then subtract.
$
   = 45 - [38 - \{ 60 \div 3 - 3 \div 3\} ] \\
   = 45 - [38 - \{ 20 - 1\} ] \\
   = 45 - [38 - 19] \\
 $
Step 3: Now, we have to solve the large bracket of the given expression in which we have to subtract the remaining terms.
$
   = 45 - 19 \\
   = 26 \\
 $

Hence, with the help of BODMAS rule we have obtained the value or simplified the given expression $45 - [38 - \{ 60 \div 3 - (6 - 9 \div 3) \div 3\} ] = 26$

Note:
In the BODMAS rule O belongs to order that means power and roots but before that we have to solve the terms inside the brackets first smaller after that curly and after that large bracket.
The order of operation is a set of standard rules that reflect convention about which process to perform to evaluate as a given numeric expression.