Question

If \[ + \] means \[ \div \] , \[ \div \] means \[ - \] , \[ - \] means \[ \times \] , \[ \times \] means \[ + \] , then \[12 + 6 \div 3 - 2 \times 8 = ?\]
A) \[ - 2\]
B) 2
C) 4
D) 8

Answer 1

Hint:
Here, we have to evaluate the given with the given rules. We will use the BODMAS rule to evaluate the given. BODMAS is an acronym and it stands for Bracket, Order, Division, Multiplication, Addition, and Subtraction. We will rewrite the equation by exchanging the mathematical operation as per given condition and then simplifying accordingly to get the required answer.

Complete step by step solution:
We have to evaluate for \[12 + 6 \div 3 - 2 \times 8\].
We are given that addition means division, division means subtraction, subtraction means multiplication and multiplication means addition.
By interchanging the signs of the equation according to the conditions given, the equation turns into \[12 \div 6 - 3 \times 2 + 8\]
By applying the BODMAS rule,
First, by performing the division, we have
\[ \Rightarrow 12 \div 6 - 3 \times 2 + 8 = 2 - 3 \times 2 + 8\]
Next, performing the multiplication, we have
\[ \Rightarrow 12 \div 6 - 3 \times 2 + 8 = 2 - 6 + 8\]
Next, performing the addition, we have
\[ \Rightarrow 12 \div 6 - 3 \times 2 + 8 = 10 - 6\]
Next, performing the subtraction, we have
\[ \Rightarrow 12 \div 6 - 3 \times 2 + 8 = 4\]

Therefore, \[12 \div 6 - 3 \times 2 + 8 = 4\]

Note:
An arithmetic expression is an expression that involves multiple operations such as addition, subtraction, multiplication, and division. In certain regions, PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction) is used, which is the synonym of BODMAS. It explains the order of operations to be performed while solving an expression. According to BODMAS rule, if an expression contains brackets ((), {}, []) we have first to solve or simplify the bracket followed by ‘order’ (that means powers and roots, etc.), then division, multiplication, addition and subtraction from left to right. Solving the problem in the wrong order will result in a wrong answer.