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Chapter 1: Problem 26

Find each sum. $$ -8+[9+(-2)] $$

Short Answer

Expert verified
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Step by step solution

01

Identify the Innermost Bracket

Locate the innermost bracket that needs to be solved first. In this case, it is \(9 + (-2)\).
02

Compute the Innermost Bracket

Add the numbers inside the innermost bracket: \(9 + (-2) = 7\).
03

Replace the Innermost Bracket with its Result

Replace \(9 + (-2)\) with its result: \(-8 + 7\).
04

Compute the Final Sum

Add the remaining numbers: \(-8 + 7 = -1\).

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Key Concepts

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

Order of Operations
When solving math problems, it's crucial to use the correct order of operations. Orders of operations is a set of rules that ensure we get accurate results. These rules are also known by the acronym PEMDAS:
  • P for Parentheses
  • E for Exponents
  • M/D for Multiplication and Division (left to right)
  • A/S for Addition and Subtraction (left to right)

In the example problem, the first step involved solving the innermost bracket because parentheses come first in PMDAS. This ensures we solve smaller parts of the problem correctly before dealing with the whole expression. Knowing this ordering avoids mistakes.
Brackets in Mathematics
Brackets play a key role in mathematics by grouping parts of an expression together. They tell us which operations to perform first. There are different types of brackets like round brackets \( ( ) \), square brackets \[ [ ] \], and curly braces \{ \}. Each type can be used for clarity and organization.
In the example \(-8 + [9 + (-2)] \), we start with the innermost bracket \(9 + (-2)\). By focusing on the brackets, we simplify complex equations into manageable steps. Ignoring brackets can lead to incorrect answers. As you proceed, always handle the innermost brackets first.
Positive and Negative Numbers
Understanding how to add and subtract positive and negative numbers is vital in mathematics. Positive numbers are greater than zero, while negative numbers are less than zero. The number line can be a helpful visual aid:
  • To add a positive number, move to the right.
  • To add a negative number, move to the left.

In the given problem, \(9 + (-2)\) means we move 2 steps left from 9 on the number line, giving us 7. After replacing the bracket with its result, we then handle the remaining operation \(-8 + 7\), which results in -1. Always remember that subtracting a positive number is like adding a negative number and vice versa.

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Most popular questions from this chapter

Perform each indicated operation. $$ 6-(-8+3) $$

Solve each problem. A pilot announces to the passengers that the current altitude of their plane is \(34,000\) ft. Because of turbulence, the pilot is forced to descend \(2100 \mathrm{ft}\). Write the new altitude as a signed number.

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

The two tables show the heights of some selected mountains and the depths of some selected trenches. Use the information given to answer. \( \)\begin{array}{|l|c|}\hline \text { Mountain } & {\text { Height (in feet) }} \\\ {\text { Foraker }} & {17,400} \\ {\text { Wilson }} & {14,246} \\\ {\text { Pikes Peak }} & {14,110} \\ \hline\end{array} $$ \begin{array}{|l|c|}\hline\text {} & {\text { Depth }( \text { in feet } } \\ {\text { Trench }} & {\text { as a negative number }} \\ {\text { Philippine }} & {-32,995} \\ {\text { Cayman }} & {-24,721} \\ {\text { Java }} & {-23,376} \\ \hline \end{array} $$ What is the difference between the height of Mt. Foraker and the depth of the Philippine Trench?

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. \(-15,29,8,-6\)
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