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Chapter 1: Problem 42

Find the value of each expression. $$ 30-3(4+2) $$

Short Answer

Expert verified
12

Step by step solution

01

- Simplify Inside Parentheses

First, simplify the expression inside the parentheses. Calculate \(4 + 2 = 6\)
02

- Multiply

Next, multiply the result by 3 as indicated outside the parentheses. Calculate \(3 \times 6 = 18\)
03

- Subtract

Lastly, subtract the multiplication result from 30. Calculate \(30 - 18 = 12\)

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Key Concepts

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

Order of Operations
The order of operations is a set of rules that defines the correct sequence to evaluate a mathematical expression. Remember the acronym PEMDAS - Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). By following PEMDAS, we ensure the accuracy of our calculations.
For example, in the expression given \(30 - 3(4 + 2)\), we must first simplify the inside of the parentheses before performing any other operations. This method helps eliminate any ambiguity in the calculation process and provides a clear pathway to the correct solution.
Parentheses Simplification
Parentheses are used in mathematics to group parts of an expression that should be evaluated first. In our exercise, \(4 + 2\) is inside parentheses. Following the order of operations, we solve the expression within the parentheses first.
Starting with \(4 + 2\), we get the result 6. This step transforms our original problem into a simpler one: \(30 - 3 \times 6\). Parentheses simplification is crucial because it changes the expression and sets the stage for subsequent operations.
Multiplication and Subtraction
After simplifying inside the parentheses, we proceed with multiplication and subtraction. According to the order of operations, multiplication comes before subtraction. Here, we multiply the result of the parentheses by 3.
For \(3 \times 6\), we get 18. Next, we tackle the subtraction: \(30 - 18\). Subtracting 18 from 30 leaves us with 12.
  • Multiplication helps us scale numbers effectively.
  • Subtraction allows us to find the difference between numbers.
Both operations are fundamental in simplifying complex mathematical expressions.

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Most popular questions from this chapter

To find the average (mean) of a group of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. All even integers between \(-18\) and \(4,\) inclusive

Find each difference. $$ -\frac{5}{6}-\frac{1}{2} $$

Solve each problem. Based on 2020 population projections, New York will lose 5 seats in the U.S. House of Representatives, Pennsylvania will lose 4 seats, and Ohio will lose 3 . Write a signed number that represents the total number of seats these three states are projected to lose.

To find the average (mean) of a group of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. \(18,12,0,-4,\) and \(-10\)

Write a numerical expression for each phrase and simplify. \(-2\) added to the sum of \(-18\) and 11
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