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Chapter 1: Problem 111

Perform these computations. $$|-15|$$

Short Answer

Expert verified
15

Step by step solution

01

Understanding Absolute Value

Absolute value represents the distance of a number from zero on the number line, regardless of direction. It is always a non-negative number.
02

Remove the Negative Sign

Since absolute value ignores whether the number is positive or negative, simply remove any negative signs. In this case, remove the negative sign from -15.
03

Determine the Result

After removing the negative sign, the absolute value of -15 is 15.

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Key Concepts

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

number line
In mathematics, a number line is a straight line where each point represents a unique real number. Imagine it as a ruler stretching infinitely in both directions. The center of this line is marked by the number 0, also known as the origin. Numbers to the right of 0 are positive, and those to the left are negative. Each placement on the number line showcases a number鈥檚 value, and it helps visualize operations and absolute values.
non-negative numbers
Non-negative numbers are all the numbers that are either positive or zero. This term specifically excludes any negative numbers. In the context of absolute value, the result is always a non-negative number. Absolute values turn negative numbers positive by ignoring the direction and only considering the magnitude. For example, \(|-15| = 15\). Non-negative numbers are fundamental in absolute value operations because they represent true distances without considering direction.
distance from zero
The absolute value of a number can be thought of as its distance from zero on the number line. Distance, by definition, is always a non-negative quantity. When calculating absolute value, the focus is purely on how far a number is from zero, not the direction it is in. For instance, both 15 and -15 have an absolute value of 15, highlighting that they are both 15 units away from zero. This concept is crucial in solving problems involving absolute values and understanding the geometrical representation of numbers.

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