Problem 37 - Elementary Algebra

Question

\(|-25|\)

Step-by-Step Solution

Answer

25

Step 1: Understand the Absolute Value

The absolute value of a number is the distance of that number from zero on the number line, without considering direction. In other words, it is always a non-negative number.

Step 2: Apply the Absolute Value Operation

To find \(|-25|\), simply remove the negative sign from the number, because absolute value makes any negative number positive.

Step 3: Write the Final Answer

After removing the negative sign, the value is 25.

Key Concepts

number line

A number line is a straight, horizontal line that represents numbers at equal intervals. The center of the number line is usually marked by zero. Numbers to the right of zero are positive and numbers to the left are negative. This visual tool helps us understand concepts like ordering of numbers, addition, subtraction, and absolute value.
When dealing with absolute value, it is useful to see where the number is situated on the number line compared to zero. For instance, -25 is 25 units to the left of zero while 25 is 25 units to the right. Both these numbers are, therefore, at an equal distance from zero.

non-negative numbers

Non-negative numbers are numbers that are either positive or zero. They do not include any negative numbers. The absolute value of any number is always non-negative because it measures distance, which can’t be negative.
When you take the absolute value of -25, you get 25. This is because absolute value turns any negative number into its non-negative counterpart by removing the negative sign. It's important to remember that even zero is considered a non-negative number since it represents no distance from zero on the number line.

distance from zero

Distance from zero is a key concept in understanding absolute value. It refers to how far a number is from zero on the number line. For example, both -25 and 25 are exactly 25 units away from zero.
When we talk about absolute value, we are actually measuring this distance, and we always express it as a non-negative number. This helps simplify working with numbers, especially in various fields like physics and engineering, where distance and magnitude are crucial.
By redefining -25 as 25 through absolute value, we are acknowledging that distance cannot be negative, making mathematical operations more intuitive.