Question

Evaluate the following expression $4 - 7 \div (3 + 1) - 3 - 2 \times (5 - 9) + 1$. By how much does the value of the expression change if the parentheses are removed?

Answer 1

Hint: In the given question, we have been asked to solve the given question keeping in mind the order of operations. In order to proceed with the following question we need to be aware of the BODMAS rule. BODMAS is an acronym for the terms Brackets, Orders, Division, Multiplication, Addition and Subtraction. This rule states that if an expression contains brackets then solve the brackets in order, then division, multiplication, addition and subtraction.

Complete step by step solution:
We are given,
$4 - 7 \div (3 + 1) - 3 - 2 \times (5 - 9) + 1$
Now by using BODMAS rule we’ll solve the brackets first
$ \Rightarrow 4 - 7 \div 4 - 3 - 2 \times ( - 4) + 1$
Then, we’ll divide the terms associated by division
$ \Rightarrow 4 - 1.75 - 3 - 2 \times ( - 4) + 1$
Then, we’ll multiply the terms associated by multiplication
$ \Rightarrow 4 - 1.75 - 3 + 8 + 1$
Then, we’ll add the terms associated by addition
$ \Rightarrow 4 - 1.75 - 3 + 9$
Then, we’ll subtract the terms associated by subtraction
$ \Rightarrow 8.25$
This is the required answer.
When the parentheses are removed
$4 - 7 \div 3 + 1 - 3 - 2 \times 5 - 9 + 1$
First we’ll divide the terms associated by division
$ \Rightarrow 4 - 2.34 + 1 - 3 - 2 \times 5 - 9 + 1$
Then, we’ll multiply the terms associated by multiplication
$ \Rightarrow 4 - 2.34 + 1 - 3 - 10 - 9 + 1$
Then, we’ll add and subtract the terms
$ \Rightarrow - 18.34$
This is the answer when brackets are removed from the expression.
The change in the value of expression when parentheses is removed would be-
$
   \Rightarrow 8.25 - ( - 18.34) \\
   \Rightarrow 26.59 \\
 $
The value has changed by $26.59$ units.

Note: You need to keep in mind that the “O” in BODMAS stands for order, which refers to all the terms which have powers, square roots etc. The order of brackets should be (), {}, [].Parentheses is another word for brackets. Also the order of solving any expression is from left to right direction, solving from right to left direction will give you incorrect answer.