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Chapter 2: Problem 87

Perform the indicated operations. $$3(9-2)+4(7-2)$$

Short Answer

Expert verified
The result of the operation is 41.

Step by step solution

01

Simplify Inside Parentheses

First, simplify the expressions inside the parentheses:\[9 - 2 = 7\]\[7 - 2 = 5\]So the expression now looks like this:\[3(7) + 4(5)\]
02

Perform Multiplications

Next, perform the multiplications from the simplified terms:\[3 imes 7 = 21\]\[4 imes 5 = 20\]
03

Add the Results

Finally, add the results of the multiplications together:\[21 + 20 = 41\]

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Key Concepts

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

Order of Operations
Understanding the order of operations is fundamental in mathematics, especially when solving problems with varying operations. The common phrase to remember is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). When following the order of operations, always start with calculations inside parentheses.
In our example, we first looked at the expression inside the parentheses:
  • The expression \(9 - 2\) gives us \(7\).
  • The expression \(7 - 2\) simplifies to \(5\).
After simplifying inside the parentheses, continue through the sequence of operations with multiplication and addition. This systematic approach ensures that you simplify expressions accurately.
Simplifying Expressions
The art of simplifying expressions involves breaking down complex equations into simpler, more manageable forms. Initially, it's crucial to tackle the components within the parentheses, as they are prioritized by the order of operations. As demonstrated:
  • The simplification of \(9 - 2\) led to \(7\).
  • Similarly, \(7 - 2\) became \(5\).
After the parentheses are addressed, the expression \(3(9-2)+4(7-2)\) reduces to \(3(7) + 4(5)\). Simplifying makes further calculations straightforward by reducing clutter and focusing only on necessary operations at each step.
Multiplication and Addition
After simplifying expressions, tackling multiplication and addition completes the process of evaluation. In our exercise, the multiplication is crucial because it's the next operator after simplifying the parentheses:
  • Calculate \(3 \times 7 = 21\).
  • Then, compute \(4 \times 5 = 20\).
Once these two parts are handled separately, they lead us to the final operation 鈥� addition. Simply add the results of the multiplications to conclude:\[21 + 20 = 41\].
This sequence underscores the order of operations where multiplication is prioritized before moving to addition, ensuring accuracy in your calculations.

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Most popular questions from this chapter

Add or subtract. $$276+32+4,005$$

Profit and Loss You own a small business which provides computer support to homeowners who wish to create their own in-house computer network. In addition to setting up the network you also maintain and troubleshoot home PCs. Business gets off to a slow start. You record a profit of \(\$ 2,298\) during the first quarter of the year, a loss of \(\$ 2,854\) during the second quarter, a profit of \(\$ 3,057\) during the third quarter, and a profit of \(\$ 1,250\) for the last quarter of the year. Do you end the year with a net profit or a net loss? Represent that profit or loss as a positive or negative value.

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