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Chapter 1: Problem 38

Add. $$ (-6)+(-8) $$

Short Answer

Expert verified
-14

Step by step solution

01

Understand negative numbers

Negative numbers are values less than zero. They are often represented with a minus sign (-) in front.
02

Identify the numbers to be added

Identify the numbers in the problem. Here, the numbers are -6 and -8.
03

Add the absolute values

First, add the absolute values of the numbers. The absolute value of -6 is 6, and the absolute value of -8 is 8. So, 6 + 8 = 14.
04

Apply the sign

Since both numbers are negative, the result will also be negative. Therefore, the solution is -14.

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Key Concepts

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

negative numbers
Negative numbers are values that are less than zero and are represented with a minus sign (-) in front of them. They are used to represent values below zero, such as temperatures in cold climates, bank overdrafts, or depths below sea level. In the exercise, -6 and -8 are both negative numbers because they each have a minus sign.

To better understand negative numbers, think of them as steps going down a staircase. If zero is the top step, then moving down 6 steps means you are at -6. Similarly, moving down 8 more steps means you are at -14. This visual helps in grasping the idea of adding negative numbers.
absolute value
Absolute value is the distance a number is from zero on the number line, regardless of direction. For instance, the absolute value of -6 is 6, and the absolute value of -8 is 8. When adding negative numbers, the absolute values are what you focus on for the addition process.

In the exercise, the absolute values of -6 and -8 are added together: 6 + 8 = 14. After calculating the absolute values, you then apply the sign rules to determine the final result.
sign rules in addition
When adding numbers, especially those with different signs, it's essential to follow the sign rules to get the correct result. Here's a quick guide:
  • Adding two positive numbers results in a positive number.
  • Adding two negative numbers results in a negative number.
  • When adding a positive number and a negative number, subtract the smaller absolute value from the larger absolute value, then take the sign of the number with the larger absolute value.

Since both numbers in the exercise (-6) and (-8) are negative, we add their absolute values (6 + 8 = 14) and then apply the sign (negative). Therefore, the solution is -14.

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Most popular questions from this chapter

Write an equivalent expression using the distributive law. $$ 9 a(b-c+d) $$

Find an equivalent expression by factoring. $$ 13 t-143 $$

Calculate using the rules for order of operations. If an expression is undefined, state this. $$ -(-3)^{2} $$

Classify each statement as either true or false. The following sets are used: \(\mathrm{N}=\) the set of natural numbers; \(W=\) the set of whole numbers; \(\mathbb{Z}=\) the set of integers; \(\mathbb{C}=\) the set of rational numbers; \(\mathrm{H}=\) the set of irrational numbers; \(\mathrm{R}=\) the set of real numbers. $$ 196 \in \mathbb{N} $$

Use set-builder notation to write each set. The set of all even numbers between 9 and 99
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