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Chapter 1: Problem 3

The additive inverse of every negative number is a (negative / positive) number.

Short Answer

Expert verified
Positive

Step by step solution

01

Understand Additive Inverse

The additive inverse of a number is a number that, when added to the original number, results in zero. Mathematically, for a number 'a', its additive inverse is '-a'.
02

Identify the Given Number

We are given a negative number. Let鈥檚 denote this negative number as '-a', where 'a' is a positive value.
03

Determine the Additive Inverse

The additive inverse of '-a' is '-(-a)'. Simplifying this, we get '-(-a) = a'.
04

Characterize the Result

Since 'a' is a positive number (because 'a' is positive by definition), the additive inverse of '-a' is thus a positive number.

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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 are numbers that are less than zero. These numbers have a minus sign (-) in front. For example, -3, -7, and -15 are all negative numbers.

Negative numbers are used to represent the following:
  • Debt or losses in finances
  • Temperatures below freezing
  • Elevations below sea level
Negative numbers play a crucial role in mathematics, especially when working with equations and different operations like addition and subtraction.
Understanding Positive Numbers
Positive numbers are numbers that are greater than zero. They have no sign or a plus sign (+) in front. For example, 5, 23, and +8 are all positive numbers.

Positive numbers are used to represent:
  • Gains or profits in finances
  • Temperatures above freezing
  • Heights above sea level
In basic arithmetic, positive numbers are straightforward and easy to work with because they follow the usual 'addition makes larger' rule.
Zero Property in Mathematics
The Zero Property is a fundamental concept in mathematics. This property indicates that the sum of any number and zero is that number itself. For example, 7 + 0 = 7 and -9 + 0 = -9.

The Zero Property is useful because:
  • It simplifies equations and calculations
  • It is the foundation of the idea of additive inverses
In additive inverses, the Zero Property helps us understand that if you add a number to its inverse, the result is always zero. For example, 5 and -5 are additive inverses because 5 + (-5) = 0.

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Most popular questions from this chapter

Write each sentence as an equation, using \(x\) as the variable. Then find the solution of the equation from the set of integers between -12 and \(12,\) inclusive. An integer is divisible by 2 if its last digit is divisible by \(2,\) and not otherwise. (a) Is 3,473,986 divisible by \(2 ?\) (b) Is 4,336,879 divisible by \(2 ?\)

Solve each problem. A pilot announces to the passengers that the current altitude of their plane is \(34,000 \mathrm{ft}\). Because of turbulence, the pilot is forced to descend \(2100 \mathrm{ft}\). Write the new altitude as a signed number.

Use the distributive property to rewrite each expression. $$ 7(z-8) $$

A manufacturer has fixed costs of \(\$ 1000\) to produce gizmos. Each gizmo costs \(\$ 5\) to make. The fixed cost to produce gadgets is \(\$ 750,\) and each gadget costs \(\$ 3\) to make. Write an expression for the cost to make \(y\) gadgets.

Write a numerical expression for each phrase, and simplify the expression. The product of 12 and the difference of 9 and -8
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