Chapter 1.1, Problem 39STP

To determine

To find: to evaluate the expression correctly what the person R has done differently

Answer to Problem 39STP

The correct answer is C.

Explanation of Solution

Given:

  A. Multiplied $\left(96÷3\right)by\left(4+7\right)$

  B. Divided $\text{96 by }\left(3\times 11\right)$

  C. Multiplied $\left(96÷3\right)by\text{ 4 and added 7}$

  D. Divided $\text{96 by }\left(4+7\right)$

Rusty is evaluating $96÷3\times 4+7$ as shown below

  $\begin{array}{l}96÷3\times 4+7\\ 3\times 4=12\\ 96÷12=8\\ 8+7=15\end{array}$

Calculation:

Her evaluation is incorrect as while evaluating she did not followed the rules for order ofoperation.

She should have followed the rules for the order of operations, which is as follows.

Step 1. Evaluate the expressions inside the grouping symbolsStep 2. Multiply and/or divide in order from left to right.

Step 3. Add and/or subtract in order from left to right.

So, this expression contains three operations namely division, multiplication and addition.

By rules for the order of operations, multiply and/or divide firstly in order from left to right. And addition is done after that.

Now on looking at the expression, while going from left to right, division comes before multiplication so divide first and then multiply and then add.

Thus the correct evaluation would be as follows:

  $\begin{array}{l}96÷3\times 4+7=\left(96÷3\right)\times 4+7\\ =32\times 4+7\\ =128+7\\ =135\end{array}$

Thus the correction answer is C.

As, in this option only the order is followed as shown above.

Conclusion:

Therefore, the correction answer is C.