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Chapter 0: Problem 39

Give (a) the additive inverse and (b) the absolute value of each number. $$ -12 $$

Short Answer

Expert verified
(a) 12, (b) 12

Step by step solution

01

Understand the Problem

We need to find both the additive inverse and the absolute value of the given number -12.
02

Find the Additive Inverse

To find the additive inverse of a number, switch the sign. The additive inverse of -12 is 12.
03

Find the Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. The absolute value of -12 is 12.

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Key Concepts

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

additive inverse
The additive inverse of a number is a concept that helps us understand how to return to zero by adding two numbers. Think of it as the number you need to add to your given number to make the sum equal zero.
Example: The additive inverse of -12.
  • Take the number -12.
  • To find its additive inverse, you switch the sign.
  • The additive inverse of -12 is 12 because -12 + 12 = 0.
Simple, isn鈥檛 it?
Remember, the additive inverse of a positive number is negative, and for a negative number, it is positive.
absolute value
The absolute value of a number is its distance from zero on the number line without considering the direction. This means the absolute value measures how far the number is from zero, always as a positive value.
Example: The absolute value of -12.
  • Look at the number -12.
  • To find its absolute value, you ignore the negative sign.
  • The absolute value of -12 is 12 because -12 is 12 units away from zero.
Doesn't matter if the number is positive or negative鈥攁bsolute value is always non-negative.
number line
A number line is a straight line that has numbers placed at equal intervals along its length. It extends infinitely in both positive and negative directions, allowing us to visualize numbers and their relationships.
Here鈥檚 how we use it:
  • Every point on the number line corresponds to a unique number.
  • Zero is at the center, with positive numbers to the right and negative numbers to the left.
  • Finding the absolute value on a number line is like measuring the distance of a point from zero.
Example: For the number -12, you would locate -12 on the number line, then count its distance to zero, which is 12 units.

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