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Chapter 1: Problem 57

Perform each indicated operation. $$ 7+2(4-1) $$

Short Answer

Expert verified
13

Step by step solution

01

Solve inside the parentheses

First, solve the expression inside the parentheses. Here, we have \(4-1\). Calculate \(4-1\): \[4 - 1 = 3\]
02

Multiply by the number outside the parentheses

Next, multiply the result from step 1 by the number outside the parentheses. The expression now is \(2 \times 3\). Calculate \(2 \times 3\): \[2 \times 3 = 6\]
03

Add the remaining number

Finally, add the result from step 2 to the remaining number. The expression now is \(7 + 6\). Calculate \(7 + 6\): \[7 + 6 = 13\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Parentheses
Parentheses are used in mathematical expressions to indicate that the operations enclosed within them should be performed first. This is crucial because the order in which you perform operations can significantly affect the outcome. For instance, in the expression given: $$7 + 2(4 - 1)$$ We must first address the operation within the parentheses, which is \( 4 - 1 \). This ensures that we accurately follow the order of operations and reach the correct result. Failing to handle parentheses first can lead to incorrect calculations.
Multiplication
After solving the operations within the parentheses, the next step is multiplication. In our example, once we have calculated \( 4 - 1 = 3 \), we must multiply this result by the number immediately outside the parentheses. In our case, that's \( 2 \times 3 \). This step is critical because multiplication must be performed before moving on to addition or subtraction. If we skip this order, we will not get the correct result.
Addition
Once we have completed any operations inside parentheses and any multiplications, we move on to the addition step. In our expression, this is \( 7 + 6 \), which results from multiplying \( 2 \times 3 \). Addition is the final step and ensures we arrive at the correct result when all previous steps have been properly executed. By following these steps: solving parentheses first, then multiplication, and finally addition, we get the correct answer, \( 13 \).

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