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Chapter 1: Problem 41

Find each sum. $$ [-4+(-3)]+[8+(-1)] $$

Short Answer

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Step by step solution

01

Add the numbers inside the first bracket

First, add the numbers inside the first bracket: ewline x = -4 + (-3) ewline -4 + (-3) is the same as -4 - 3, which equals -7.
02

Add the numbers inside the second bracket

Next, add the numbers inside the second bracket: ewline x = 8 + (-1) ewline 8 + (-1) is the same as 8 - 1, which equals 7.
03

Add the results from the two brackets

Finally, add the results obtained from the previous steps: ewline x = -7 + 7 ewline -7 + 7 equals 0.

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Key Concepts

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

Integer Addition
Adding integers involves combining numbers which can be either positive or negative. It's essential to understand the basic rules:
  • When you add two positive integers, the result is positive.
  • When you add two negative integers, the result is negative.
  • When you add a positive and a negative integer, subtract the smaller absolute value from the larger absolute value and take the sign of the larger absolute value.
In our exercise, we need to add both positive and negative numbers.
Negative Numbers
Negative numbers represent values less than zero and are used in many mathematical contexts. When adding negative numbers:
  • Think of moving further left on the number line.
  • For example, adding -4 and -3 means moving 4 steps left from zero, then 3 more steps left, landing you at -7.
This logic also applies when dealing with more complex expressions. In our exercise, for the first bracket, we combine -4 and -3 to get -7.
Combining Like Terms
When solving algebraic problems, combining like terms is essential. This means adding or subtracting numbers or expressions that have the same variables or are constants. In our example, after solving each bracket individually, we are left with the constants -7 and 7. Combining these two like terms results in:
  • Adding together -7 and 7 equals 0.
Combining like terms helps simplify mathematical expressions and reach the final solution efficiently.

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Most popular questions from this chapter

Decide whether each statement is true or false. \(|13-8| \leq|7-4|\)

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} $$ \begin{array}{|l|c|}\hline\text {} & {\text { Depth }( \text { in feet } } \\ {\text { Trench }} & {\text { as a negative number }} \\ {\text { Philippine }} & {-32,995} \\ {\text { Cayman }} & {-24,721} \\ {\text { Java }} & {-23,376} \\ \hline \end{array} $$ How much deeper is the Cayman Trench than the Java Trench?

Find each difference. $$ -\frac{3}{4}-\frac{5}{8} $$

Perform each indicated operation. $$ (9-3)-15 $$

In August, Susan Goodman began with a checking account balance of \(\$ 904.89\). Her checks and deposits for August are as follows: $$ \begin{array}{|r|r|} \hline \text { Checks } & \text { Deposits } \\ \hline \$ 35.84 & \$ 85.00 \\ \$ 26.14 & \$ 120.76 \\ \$ 3.12 & \\ \hline \end{array} $$ Assuming no other transactions, what was her account balance at the end of August?
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