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Chapter 1: Problem 104

\(-2+(-5)\)

Short Answer

Expert verified
The sum of -2 and -5 is -7.

Step by step solution

01

Identify the Problem

The problem is to add two negative integers: -2 and -5.
02

Recall the Rule for Adding Negatives

When adding two negative numbers, the sum is also negative. This is because you are combining two amounts of negative value.
03

Add the Absolute Values

Add the absolute values of the numbers, ignoring the negative signs for now: \[ |2| + |5| = 2 + 5 = 7 \]
04

Apply the Negative Sign

Since both original numbers were negative, the sum of their absolute values will also be negative. Therefore, the answer is: \[ -7 \]

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Key Concepts

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

Integers
Integers are whole numbers that can be positive, negative, or zero. They do not include fractions or decimals. The set of integers is denoted by the symbol \( \mathbb{Z} \). It includes numbers like
  • -3, -2, -1
  • 0, 1, 2, 3
Adding integers follows specific rules that differ depending on whether the integers are positive or negative. For instance:
  • Positive + Positive = Positive
  • Negative + Negative = Negative
  • Positive + Negative can be either positive or negative, depending on the number with the greater absolute value
To solve problems that involve integers, like adding negative numbers, it's essential to understand these fundamental properties and relationships within the set of integers.
Absolute Values
The absolute value of a number is its distance from zero on the number line, without considering direction. It is always a non-negative number. Absolute value is denoted by vertical bars, like this: \(|x|\). For any integer \(x\):
  • \(|x| = x\) if \(x \geq 0\)
  • \(|x| = -x\) if \(x < 0\)
This means that the absolute value of -3 is 3 \((|-3| = 3)\), and the absolute value of 3 is also 3 \((|3| = 3)\). Absolute values are crucial when adding negative numbers because they help us determine the magnitude of each number involved, ignoring their signs initially.
Mathematical Rules
When adding negative numbers, it's essential to apply the correct mathematical rules to obtain the right result. Start by recalling that adding two negative numbers results in a negative sum. Here's the reasoning:
  • You add the absolute values of the numbers.
  • After finding the sum of the absolute values, apply the negative sign to the total.
For example, to solve \(-2 + (-5)\), calculate:1. \(|2| + |5| = 2 + 5\)2. The result is 7, but the sum must also be negative.3. Therefore, \(-2 + (-5) = -7\).These rules simplify the process by consistently guiding you toward the negative sum when two negatives are combined. Understanding these mathematical principles ensures precise and accurate computation of integer-related problems.

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Most popular questions from this chapter

Simplify each algebraic expression and then evaluate the resulting expression for the given values of the variables. \(-3 x+7 x+4 x-2 x-x\) for \(x=-13\)

Simplify each algebraic expression and then evaluate the resulting expression for the given values of the variables. \(5 x-6 x+x-7 x-x-2 x\) for \(x=-15\)

Find the value of \(\frac{h\left(b_{1}+b_{2}\right)}{2}\) for each set of values for the variables \(h, b_{1}\), and \(b_{2}\). (Subscripts are used to indicate that \(b_{1}\) and \(b_{2}\) are different variables.) \(h=8, b_{1}=17\), and \(b_{2}=24\)

Simplify each algebraic expression by combining similar terms. $$-6 m-m+17 m$$

Insert parentheses so that \(36+12 \div 3+3+6 \cdot 2\) is equal to 38 .
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