Problem 3 - Beginning and Intermediate Algebra

Question

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

Step-by-Step Solution

Answer

Positive

Step 1: 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'.

Step 2: Identify the Given Number

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

Step 3: Determine the Additive Inverse

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

Step 4: 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.

Key Concepts

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.