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Chapter 1: Problem 82

What are additive inverses?

Short Answer

Expert verified
The additive inverse of a number is the number that, when added to the original number, results in zero. For any number \(a\), its additive inverse is \(-a\).

Step by step solution

01

Understand the term 'inverse'

In mathematics, an 'inverse' of a number is something that, when combined with the original number using a specific operation, reverses the effect of that operation. In other words, if you apply an operation to a number and its inverse, you should get the identity element for that operation.
02

Recognize the additive identity

For addition, the identity element is zero because adding zero to any number does not change the number. Symbolically, if \(a\) is any number, then \(a + 0 = a\).
03

Define the additive inverse

Therefore, the additive inverse of a number is the number that, when added to the original number, results in zero. Symbolically, the additive inverse of a number \(a\) is often written as \(-a\) because \(a + (-a) = 0\).

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Most popular questions from this chapter

The list shows a pattern for various products. $$\begin{aligned}2(-3) &=-6 \\\1(-3) &=-3 \\\0(-3) &=0 \\\\-1(-3) &=3 \\\\-2(-3) &=6 \\\\-3(-3) &=9 \\\\-4(-3) &=? \end{aligned}$$ Use this pattern to find \(-4(-3)\)

Perform the indicated subtraction. $$13-(-13)$$

Identify the terms in each algebraic expression. $$-3 x-8 y$$

Perform the indicated subtraction. $$-2.06-(-2.06)$$

Simplify each series of additions and subtractions. $$-823-146-50-(-832)$$
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