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Chapter 0: Problem 69

Simplify each expression. $$ 6|4-5|-24 \div 3 $$

Short Answer

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Step by step solution

01

Simplify the Absolute Value

Calculate the value within the absolute value symbols first. Inside the absolute value, we have \(4 - 5\), which equals \(-1\). The absolute value of \(-1\) is \(|-1| = 1\). So the expression becomes \(6 \times 1 - 24 \tdiv 3\).
02

Perform Multiplication

Next, perform the multiplication. \(6 \times 1 = 6\). The expression now is \(6 - 24 \tdiv 3\).
03

Perform Division

Now, perform the division. \(-24 \tdiv 3 = -8\). The expression is now \(6 - 8\).
04

Perform the Subtraction

Finally, perform the subtraction. \(6 - 8 = -2\).

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Key Concepts

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

Absolute Value
The absolute value of a number is its distance from zero on the number line. It is always a non-negative number. For instance, the absolute value of \(-1\) is \(1\) because \(-1\) is one unit away from zero, though in the negative direction. Absolute value is denoted by vertical bars, \(|x|\). So, \(|-1| = 1|\). When simplifying expressions, always handle the contents inside the absolute value bars first.
Order of Operations
The order of operations is crucial in simplifying algebraic expressions correctly. It is remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). For example, in the expression \(6|4-5|-24 \div 3\), follow these steps:
  • First, compute inside the absolute value bars: \(4-5 = -1\) then \(|-1| = 1\).
  • Next, handle multiplication and division from left to right: \(6 \times 1 = 6\) and \(-24 \div 3 = -8\).
  • Lastly, handle addition or subtraction: \(6 - 8 = -2\).
This ensures the expression is simplified correctly.
Multiplication and Division in Expressions
In algebra, multiplication and division should be performed from left to right as they appear in the expression. They are of equal priority. Consider this example: \(6 \times 1 - 24 \div 3 \).
  • First, do the multiplication: \(6 \times 1 = 6\).
  • Then, handle the division: \(-24 \div 3 = -8\).
This step ensures you do not accidentally mix up operations and get incorrect results.
Subtraction in Algebra
Subtraction in algebra may seem simple, but it's essential to know its place in the order of operations. In the expression \(6 - 8\), you directly subtract after completing all necessary multiplication and division. This step-by-step method prevents mistakes. After you have simplified all components leading up to it, just subtract the numbers straightforwardly. In this example, \(6 - 8 = -2\).

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Most popular questions from this chapter

Determine whether each statement is true or false. The absolute value of any number is the same as the absolute value of its additive inverse.

Solve each problem. The table shows the percent change in population from 2010 through 2016 for selected metropolitan areas. $$ \begin{array}{|l|c|} \hline \text { Metropolitan Area } & \text { Percent Change } \\ \hline \text { Detroit } & -5.8 \\ \text { Houston } & 9.7 \\ \text { Las Vegas } & 8.3 \\ \text { New Orleans } & 13.9 \\ \text { Phoenix } & 11.6 \\ \text { Toledo } & -3.0 \\ \hline \end{array} $$ (a) Which metropolitan area had the greatest change in population? What was this change? Was it an increase or a decrease? (b) Which metropolitan area had the least change in population? What was this change? Was it an increase or a decrease?

Simplify each expression. $$ 15+5 \cdot 2 $$

Choose the correct response. The additive inverse of \(a\) is A. \(-a\) B. 0 C. 1 D. \(\frac{1}{a}\).

Write each percent as a fraction. Give answers in lowest terms. See Example 13. $$ 47 \% $$
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