Problem 82 - Prealgebra and Introductory Algebra

Question

Find the absolute value of the number. $$-1$$

Step-by-Step Solution

Answer

The absolute value of -1 is 1.

Step 1: Identify the Number

The number provided is -1.

Step 2: Apply Absolute Value Rule

The absolute value of a number refers to its distance on the number line from 0 without considering the direction. Hence, regardless whether the number is negative or positive, its absolute value is always positive. So here, the absolute value of -1 is 1.

Key Concepts

number line

The number line is a visual representation of numbers placed along a straight horizontal line. It helps us understand the order and relative position of numbers. Numbers increase as you move to the right and decrease when you move to the left.

Imagine a ruler stretched out infinitely in both directions. The center point is zero, and numbers to the right are positive. Numbers to the left of zero are negative.

• Each point on the number line corresponds to a real number.
• This tool helps us visualize operations like addition, subtraction, and finding absolute values.
• The distance between any number and zero determines its absolute value. For example, whether you have -3 or 3, their distance from zero is 3.

Understanding how to maneuver the number line enhances basic arithmetic skills and lays the foundation for more complex math concepts.

positive numbers

Positive numbers are all the numbers greater than zero. As you move to the right of zero on the number line, you'll encounter these numbers.

Here are some characteristics of positive numbers:

• Symbolically, these numbers either have no sign or a '+' sign in front of them. For example, 5 or +5.
• They represent quantities or values that denote amounts, distances, or increases.
• They are always to the right of zero on the number line.
• Addition or multiplication involving positive numbers and zero yield positive outcomes.

As you become more comfortable with positive numbers, you'll see they form the basis for understanding more complex calculations and measures, signifying accumulation or growth.

negative numbers

Negative numbers are those less than zero, and they have a minus sign (-) in front of them. As you move left from zero on the number line, negative numbers appear.

Understanding negative numbers allows you to grasp concepts like debt or temperature drops.

• They are always preceded by a '-' sign, such as -1 or -5.
• Negative numbers tell us about a deficit, decrease, or loss in value.
• They sit to the left of zero on a number line—further left means a larger negative effect.
• Operations using negative numbers often involve reversing directions. For example, subtracting a negative number is akin to adding its positive counterpart.

Getting acquainted with how negative numbers work is crucial for balancing equations, understanding financial contexts, and solving real-world problems that involve reductions or decreases.