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Chapter 1: Problem 27

Find each sum. $$ -6+[6+(-9)] $$

Short Answer

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Step by step solution

01

- Simplify the Innermost Parentheses

Start by simplifying the expression within the innermost parentheses: Add -9: Step 1 - Simplify the Innermost Parentheses
02

- Add the Outer Operations

Now add the simplified result outer number -6 Step 2 - Add the Outer Operations

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Key Concepts

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

Integer Addition
Adding integers might feel tricky, but it's straightforward once you know the rules.
In this exercise, we need to add and subtract integers correctly to find the sum.
Let's break it down:
1. **Identify the numbers** we are working with: -6, 6, and -9.
2. **Combine integers step by step**:
- First, group the numbers together if they are within parentheses.
- Then, perform the addition or subtraction.
For example, in the expression ewline ewline ofor -6 + [6 + (-9)], first solve within the parentheses: 6 + (-9).
Now, handle the final sum by adding the outer number -6 and the result from the parentheses.
Absolute Values
Absolute values are essential in integer addition. They represent the distance a number is from zero on a number line, no matter the direction.
For instance, the absolute value of both -6 and 6 is 6.
Here鈥檚 why understanding absolute values helps with addition:
  • For positive values, it's just the number itself.
  • For negative values, it's the number without the negative sign.
In our example: 6 and -9.
The absolute value of 6: \( |6| = 6 \)
The absolute value of -9: \( |-9| = 9 \)
When adding 6 + (-9), we can think in terms of absolute values:
  • Compare absolute values: since 9 (absolute value of -9) is greater than 6 (absolute value of 6), the result takes the sign of the larger absolute value.
The sum is therefore a negative value of ewline ewline 3 \( [-(9 - 6)] \).
Order of Operations
Order of operations is crucial in mathematics. It tells us the order to solve parts of an expression.
The acronym PEMDAS helps us remember the sequence:
  • P (Parentheses)
  • E (Exponents)
  • MD (Multiplication and Division, from left to right)
  • AS (Addition and Subtraction, from left to right)
For our sum expression, -6 + [6 + (-9)], follow these steps:
1. **Solve within the parentheses first**: [6 + (-9)].
2. **Perform the addition within the brackets**: 6 + (-9) = -3
3. **Handle the remaining part of the equation**: -6 + (-3).
This step-by-step approach ensures we calculate the correct answer.
So for this exercise, following PEMDAS results in the final sum: -6 + (-3) = -9.

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Most popular questions from this chapter

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 Pikes Peak and the depth of the Java Trench?

In September, Jeffery Cooper began with a checking account balance of 904.89 Dollar. His checks and deposits for September are as follows: $$ \begin{array}{|l|c|} \hline \text { Checks } & \text { Deposits } \\ \$ 41.29 & \$ 80.59 \\ \$ 13.66 & \$ 276.13 \\ \$ 84.40 & \\ \hline \end{array} $$ Assuming no other transactions, what was his account balance at the end of September?

The operation of division is used in divisibility tests. A divisibility test allows us to determine whether a given number is divisible (without remainder) by another number. An integer is divisible by 9 if the sum of its digits is divisible by \(9,\) and not otherwise. Show that (a) \(4,114,107\) is divisible by \(9 \quad\) and \(\quad\) (b) \(2,287,321\) is not divisible by \(9 .\)

The operation of division is used in divisibility tests. A divisibility test allows us to determine whether a given number is divisible (without remainder) by another number. An integer is divisible by 4 if its last two digits form a number divisible by \(4,\) and not otherwise. Show that (a) \(6,221,464\) is divisible by 4 and \((b) 2,876,335\) is not divisible by 4

Write a numerical expression for each phrase and simplify. 19 less than the difference between 9 and \(-2\)
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