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Chapter 1: Problem 41

Add See Examples \(\ell\) through 7 . $$ -15+9+(-2) $$

Short Answer

Expert verified
The result is \(-8\).

Step by step solution

01

Identify the Numbers and Their Signs

The expression we need to evaluate is \[-15 + 9 + (-2)\]Here, we have three numbers with their respective signs: - \(-15\) is a negative number.- \(9\) is a positive number.- \(-2\) is a negative number.
02

Group and Add Negative Numbers

First, add the negative numbers together:\[-15 + (-2) = -17\]This is because when you add two negative numbers, you add their absolute values and keep the negative sign.
03

Add the Positive Number

Now, add the positive number to the sum of the negative numbers:\[-17 + 9\]When adding a positive number to a negative number, you subtract the smaller absolute value (\(9\)) from the larger absolute value (\(17\)) and keep the sign of the larger absolute value:\[-17 + 9 = -8\]

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Key Concepts

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

Understanding Negative Numbers
Negative numbers represent values less than zero, and they are typically shown with a minus sign (-) in front of the number. In mathematics, negative numbers can seem puzzling at first, but they are incredibly useful. They help us represent losses, depths, and temperatures below freezing, among other things.

When working with negative numbers:
  • Adding two negative numbers results in a more negative number. For example, \(-3\) added to \(-5\) gives us \(-8\).
  • Subtracting a negative number is equivalent to adding its positive counterpart. Think of it as reversing the absence of something.

Understanding how to manipulate negative numbers will aid greatly in solving math problems by fostering an intuition for numerically comparing values.
What is Absolute Value?
Absolute value is a concept used to express the magnitude of a number regardless of its sign. It tells us how far a number is from zero on a number line. When you see the absolute value symbol, \(|x|\), around a number, simply ignore any negative sign for calculating the magnitude.

  • The absolute value of a positive number is just the number itself, \(|9| = 9\).
  • The absolute value of a negative number is the positive version of that number, \(|-9| = 9\).
  • Absolute value helps in dealing with expressions like \(-15 + 9\) by considering the size of numbers without regard to their direction (positive or negative).

Using absolute values, we can understand the true 'size' of a number and compare or compute differences regardless of direction.
Exploring Positive Numbers
Positive numbers are numbers greater than zero and are considered to be the standard counting or natural numbers. These include all integer values without a negative sign and zero is the neutral element in this context.

When dealing with positive numbers:
  • Adding positive numbers together results in a larger number. For instance, \(5 + 3 = 8\).
  • When adding a positive number to a negative number, think of it as calculating the difference between their absolute values. The sign will depend on which absolute value is larger.

Positive numbers are intuitive for most people since they relate to quantities we encounter in everyday life such as counting objects or measuring distances.

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Most popular questions from this chapter

Perform the following operations. Write answers in lowest terms. $$ \frac{11}{35}+\frac{3}{35} $$

Decide whether the given number is a solution of the given equation. Is \(-4\) a solution of \(x-9=5 ?\)

Add or subcract as indicared. Write the answer in lower terms. See Erample 5 $$ \frac{6}{7}+\frac{1}{7} $$

If \(a\) is a positive number and \(b\) is a negative number, determine whether each statement is true or false. \(|b-a|\) is always a positive number.

Perform the following operations. Write answers in lowest terms. $$ \frac{7}{8} \div 3 \frac{1}{4} $$
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