Question

Explain \[72+12\times 3\div 8-6=20\].

Answer 1

Hint: In this type of question we have to use the concept of logical reasoning along with the BODMAS rule. The BODMAS rule is an acronym to help students remember the order of mathematical expressions – the correct order in which students have to solve math problems. BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction. In the given question students have to interpret the correct meaning of each mathematical expression to reach at the given result.

Complete step by step answer:
Now, we have to show \[72+12\times 3\div 8-6=20\] by the correct interpretation of each of the mathematical expressions.
If we consider the given equation as it is and try to simplify it then we proceed as follows:
To simplify the given equation we have to use the BODMAS rule. BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction.
Let us simplify the left side of the given equation, i.e. \[72+12\times 3\div 8-6\] by using BODMAS
\[\begin{align}
  & \Rightarrow 3\div 8=0.375\text{ Division} \\
 & \Rightarrow 0.375\times 12=4.5\text{ Multiplication} \\
 & \Rightarrow 4.5+72=76.5\text{ Addition} \\
 & \Rightarrow 76.5-6=70.5\text{ Subtraction} \\
 & \Rightarrow 72+12\times 3\div 8-6=70.5 \\
\end{align}\]
So we can clearly see that the result does not match with the required one. Hence, we have to find out the correct meaning of each of the mathematical expressions.
Now, if we interchange the expressions \[+\] and \[\div \] then the left side of the given equation becomes,
\[72\div 12\times 3+8-6\] . And if we simplify it by using BODMAS rule then we get,
\[\begin{align}
  & \Rightarrow 72\div 12=6\text{ Division} \\
 & \Rightarrow 6\times 3=18\text{ Multiplication} \\
 & \Rightarrow 18+8=26\text{ Addition} \\
 & \Rightarrow 26-6=20\text{ Subtraction} \\
\end{align}\]
Here, we can see that the result obtained matches with the required result.
Hence we have to interchange the mathematical expressions \[+\] and \[\div \] to obtain the required result.

Note: In this type of question students have to interpret the correct meaning of the mathematical expressions. If required then students may interchange the places of mathematical expressions to obtain the required result.