Chapter 1.1, Problem 38HP

To determine

To explain:why the rules for the order of operations are important.

Answer to Problem 38HP

Two different answers are obtained. So, rules for order of operation should be followed.

Explanation of Solution

Calculation:

It is very important to follow the rules for the order of operation while evaluating numericalexpressions as in math, there can be only one correct answer, so mathematicians set up some rules so that all can come up with the same correct answer. As otherwise, if everyone solves the question in the way they want then, they may end up with different answers of the same question.

For example, consider the expression $2\times 3+4$

If addition is done first, then

  $2\times 3+4=2\times 7=14$

And, if multiplication is done first, then

  $2\times 3+4=6+4=10$

So, it can be seen that two different answers for the same question is obtained. But the second answer is correct as according to the order of operation multiply first and then add.

Now, consider another expression, $31-4\times 5+6$

Now, multiplicationis done first, thus

  $31-4\times 5+6=31-20+6$

Now, after this step, if addition is done first, then

  $\begin{array}{l}31-4\times 5+6=31-20+6\\ =31-26\\ =5\end{array}$

While subtract first, then

  $\begin{array}{l}31-4\times 5+6=31-20+6\\ =11+6\\ =17\end{array}$

In this case too, two different answersare obtained but again second one is correct.

So, rules for order of operation should be followed.

Conclusion:

Therefore, two different answers are obtained. So, rules for order of operation should be followed.