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Chapter 1: Problem 40

Find each sum. $$ [-8+(-3)]+[-7+(-6)] $$

Short Answer

Expert verified
-24

Step by step solution

01

Simplify the First Expression

Add the numbers inside the first set of brackets -8 + (-3). This equals -11 because adding two negative numbers results in a sum that is the more negative.
02

Simplify the Second Expression

Add the numbers inside the second set of brackets -7 + (-6). This equals -13 for the same reason as above.
03

Add the Results of Both Simplified Expressions

Finally, add the results from Step 1 and Step 2. -11 + (-13). This equals -24 because the sum of two negative numbers is a larger negative number.

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Key Concepts

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

Basic Arithmetic Operations
Basic arithmetic operations include addition, subtraction, multiplication, and division. These operations are the foundation of all mathematical calculations.
When we talk about addition, it usually involves combining two or more numbers to get a total.
For instance, adding 2 and 3 gives us 5. This is straightforward with positive numbers. However, things can be a bit different when dealing with negative numbers, which we will explore in the next sections.
Negative Numbers Addition
Adding negative numbers might seem confusing at first, but it's quite straightforward once you understand the rules.
Here are the main points to remember when adding negative numbers:
  • Add the numbers as if they were positive.
  • Then, attach a negative sign to the sum.
For example, let鈥檚 look at (-8 + (-3)).
Ignoring the negative signs for a moment, we add 8 and 3 to get 11. Because both original numbers were negative, the result is (-11).
This is the basic principle behind the addition of all negative numbers, as demonstrated in our example problem.
Integer Operations
Integers are a set of numbers that include all positive whole numbers, their negative counterparts, and zero.
When performing operations with integers, especially with negative numbers, it is essential to remember the following rules to make calculations easier:
  • The sum of two negative integers is always negative. For instance, -8 + (-3) = -11.
  • The sum of a positive integer and a negative integer depends on their absolute values.
In our example, after simplifying the expressions within the brackets, [(-8 + (-3)) + (-7 + (-6))] becomes (-11) + (-13).
Again, following the same addition rule for negative numbers, (-11) and (-13) add up to (-24).
Familiarizing yourself with these rules will help you handle integer operations more confidently.

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Most popular questions from this chapter

Use the commutative or the associative property to complete each statement. State which property is used. See Examples I and 2. $$ 8 \cdot(6 \cdot 4)=(8 \cdot \quad) \cdot 4 $$

Find each sum. $$ -2+[5+(-1)] $$

Write each word phrase as an algebraic expression, using x as the variable. A number subtracted from seven

Solve each problem. The top of Mt. Whitney, visible from Death Valley, has an altitude of \(14,494\) ft above sea level. The bottom of Death Valley is 282 ft below sea level. Using 0 as sea level, find the difference between these two elevations.

Find each difference. $$ 8-13 $$
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