Problem 64 - Elementary and Intermediate Algebra

Question

Find each absolute value. $$|-47|$$

Step-by-Step Solution

Answer

47

Step 1: Understand Absolute Value

Absolute value is the distance of a number from zero on the number line, regardless of direction. Therefore, absolute value is always non-negative.

Step 2: Identify the Number

Here, the number given is -47.

Step 3: Apply the Absolute Value Concept

Since absolute value measures the distance from zero without considering the sign, the absolute value of -47 is 47.

Key Concepts

Number Line

The number line is a visual representation of numbers arranged in a straight line. Each point on the line corresponds to a number.

To understand placing numbers on a number line, start with 0, which is typically in the center. Moving right of 0, we have positive numbers like 1, 2, 3, and so on. Moving left, we have negative numbers like -1, -2, -3, etc.

• The further right you go, the larger the positive number.
• The further left you go, the larger the absolute value of the negative number, but with a negative sign.
• The absolute value of any number is the distance of that number from 0.

Distance from Zero

Distance from zero refers to how far away a number is from zero on the number line. This measurement is what we call absolute value.

For example, the distance from 3 to 0 is 3, and the distance from -3 to 0 is also 3. Even though -3 is to the left of 0, we measure distance as a positive value.

• Absolute value ignores whether the number is negative or positive.
• It only looks at the size of the gap or interval.
• This property makes absolute values always non-negative.

Non-Negative

Non-negative means a number is either positive or zero; it’s never negative. Non-negative numbers include all positive numbers and zero.

Absolute values are non-negative by definition because they represent distance, which can’t be negative.

• To find the absolute value, you remove any negative sign from the number.
• For example, |-47| results in 47, as you're focusing only on the magnitude, not the direction.
• Thus, the absolute value of any number is its non-negative version.