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Chapter 0: Problem 58

Perform the indicated operations. $$ |-6|+|-3|-|4|-|-8| $$

Short Answer

Expert verified
-3

Step by step solution

01

- Evaluate Absolute Values

Find the absolute values of the numbers given: |鈭�6|=6,|鈭�3|=3,|4|=4,|鈭�8|=8
02

- Substitute the Absolute Values

Replace the numbers with their absolute values in the given expression:6 + 3 - 4 - 8
03

- Perform Addition

Add the first two numbers:6 + 3 = 9
04

- Perform Subtraction

Subtract the next two numbers one by one:9 - 4 = 5,5 - 8 = -3

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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, regardless of direction. Imagine the number line like a ruler where each unit represents a step. Both 5 and -5 are 5 steps away from zero, hence their absolute values are the same, which is 5.
Absolute values eliminate the negative sign, if any. For instance:
\(|-6| = 6\)
\(|4| = 4\).
  • Remember: Absolute value is always non-negative.
addition and subtraction
Addition and subtraction are basic arithmetic operations used to combine numbers, including absolute values. When dealing with absolute values, evaluate them first and then perform the operations.
For example, with the absolute values: \(|-6| = 6\), \(|-3| = 3\), \(|4| = 4\), \(|-8| = 8\), we substitute them into the expression. Here鈥檚 the step-by-step:
\[|-6| + |-3| - |4| - |-8|\rightarrow 6 + 3 - 4 - 8\rightarrow 9 - 4 - 8\].
evaluating expressions
Evaluating expressions involves performing all indicated operations in the correct order. Follow these steps after substituting absolute values into the expression:
1. **Perform addition first:** Add 6 and 3 to get 9: \[6 + 3 = 9\].
2. **Perform subtraction next:** Subtract 4 from 9 to get 5: \[9 - 4 = 5\].
3. **Proceed with the final subtraction:** Subtract 8 from 5 to get -3: \[5 - 8 = -3\].
  • When evaluating complex expressions, always break them down into smaller, manageable steps.

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Most popular questions from this chapter

Find each square root. If it is not a real number, say so. $$ -\sqrt{0.49} $$

The distributive property can be used to mentally perform calculations. $$\begin{array}{l}38 \cdot 17+38 \cdot 3 \\\=38(17+3) \\\=38(20) \\\=760\end{array} $$Use the distributive property to calculate each value mentally. $$ 58 \cdot \frac{3}{2}-8 \cdot \frac{3}{2} $$

The distributive property can be used to mentally perform calculations. $$\begin{array}{l}38 \cdot 17+38 \cdot 3 \\\=38(17+3) \\\=38(20) \\\=760\end{array} $$Use the distributive property to calculate each value mentally. $$ 4.31(69)+4.31(31) $$

Solve each problem. The amount, in billions of dollars, that Americans spent on their pets from 2003 to 2016 can be approximated by substituting a given year for \(x\) in the following expression. $$2.493 x-4962$$ (Data from American Pet Products Manufacturers Association.) Find the amount spent in each year. Round answers to the nearest tenth. (a) 2003 (b) 2010 (c) 2016 (d) How did the amount Americans spent on their pets change from 2003 to \(2016 ?\)

Write each percent as a fraction. Give answers in lowest terms. See Example 13. $$ 2 \% $$
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