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Chapter 1: Problem 5

\(-3+(-4)\)

Short Answer

Expert verified
The result of -3 + (-4) is -7.

Step by step solution

01

Identify the Operation

The given expression is -3 + (-4). Your task is to perform addition on these two integers.
02

Understand Negative Addition

When adding two negative numbers, add their absolute values (ignoring the negative signs) and attach a negative sign to the result. For example, if you add -3 and -4, focus on 3 and 4 first.
03

Calculate the Absolute Sum

Calculate the absolute sum of the numbers: 3 + 4 = 7.
04

Attach Negative Sign

Since both original numbers were negative, attach a negative sign to the sum: The result is -7.

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Key Concepts

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

Integer Addition
Integer addition involves combining whole numbers. Numbers can be positive or negative, which influences how addition works. When you add integers:
  • If both integers are positive, the result is simply their sum.
  • If both integers are negative, like in the exercise \(-3 + (-4)\), add their absolute values and place a negative sign before the sum.
  • If one is positive and the other is negative, subtract the smaller number's absolute value from the larger number's absolute value, keeping the sign of the larger number.
Adding integers becomes straightforward with practice, focusing first on the absolute values and then determining the correct sign for the result.
Negative Numbers
Negative numbers are those less than zero and are represented with a minus sign (e.g., -1, -2, -3). Adding negative numbers follows specific rules:
  • Think of negative numbers as values moving left on a number line. Thus, adding \(-3\) and \(-4\) results in \(-7\) because you move further to the left.
  • Negative addition involves adding their magnitudes and keeping the result negative when only negative terms are involved.
Negative numbers are crucial in various real-world scenarios, such as accounting for debts and analyzing temperatures below zero.
Absolute Value
The absolute value of a number is its distance from zero on the number line, ignoring its sign. It is denoted by vertical bars, e.g., \(|-3| = 3\). When dealing with absolute values:
  • For any positive number, its absolute value is the number itself, e.g., \(|5|=5\).
  • For negative numbers, ignore the negative sign to find the absolute value, e.g., \(|-4|=4\).
  • Zero has an absolute value of zero, i.e., \(|0|=0\).
The concept of absolute value simplifies many mathematical operations by converting all numbers to positive, enabling easier comparison and calculation.

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Most popular questions from this chapter

Simplify each numerical expression. Don't forget to take advantage of the properties if they can be used to simplify the computation. $$(2)(-71)(50)$$

State the property that justifies each statement. For example, \(3+(-4)=(-4)+3\) because of the commutative property for addition. $$(-9)(17)=17(-9)$$

Simplify each algebraic expression by combining similar terms. $$-4(a+2)+6(a+8)-3(a-6)$$

State whether the expressions in each problem are equivalent and explain why or why not. \((-6 a+7 b)+11 c\) and \(7 b+(11 c-6 a)\)

State the property that justifies each statement. For example, \(3+(-4)=(-4)+3\) because of the commutative property for addition. $$-2+(5+7)=(-2+5)+7$$
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