Question

Complete the sentence. The absolute value of \(-16\) is _____________

Short answer

Answer: The absolute value of -16 is 16.

Step-by-step solution

Definition of absolute value

The absolute value of a number can be defined as the distance between the given number and zero on the number line. In other words, the absolute value of a number is the non-negative value of the given number. It is represented as \(|-16|\).

Determine the distance from zero

Since -16 is 16 units away from zero on the number line to the left, the distance between -16 and zero is 16.

Conclusion

Therefore, the absolute value of \(-16\) is 16. So, the completed sentence is: "The absolute value of \(-16\) is \(16\)."

Key concepts

number line

The number line is a visual tool that helps us understand the concept of numbers and their values more easily. It is a straight horizontal line that extends infinitely in both directions.

• On the right, numbers increase from zero towards positive infinity.
• On the left, numbers decrease as you move towards negative infinity.
• Zero is placed in the center, acting like a midpoint.

The number line is helpful in revealing the relationships between numbers. It allows us to quickly see the position of any number relative to zero. For example, if you imagine standing at zero and walking sixteen steps to the left, you would arrive at earlier mentioned number -16. This assists in understanding negative numbers and their absolute values!

distance from zero

In mathematics, understanding a number's "distance from zero" is essential when dealing with absolute values. This distance illustrates how far a number lies from zero on the number line, regardless of its direction.

To determine the distance from zero, simply count the number of steps needed to reach zero from the selected point. In our example, -16 is 16 units away from zero. This distance provides us with the absolute value, which is always a positive number.

• Negative numbers are as far from zero as their positive counterparts, just on the opposite side of the number line.
• This means that the distance from zero focuses on the size of the number, not its negative or positive sign.

Therefore, the distance from zero is a fundamental part of grasping absolute values, showcasing size without regard to direction.

non-negative value

When discussing absolute values, the term "non-negative value" is often used. This refers to values that are either positive or zero. Absolute value equates to the non-negative representation of a number.

• Negative numbers transform into positive numbers when their absolute values are taken.
• Positive numbers and zero remain unchanged, as they are already non-negative.

For instance, in the exercise, -16 becomes 16 because the absolute value operation removes the negative sign. Thus, we observe that absolute values convert any number into a non-negative form by focusing solely on a number's magnitude and disregarding its sign. This is crucial for various mathematical applications where only size matters, not direction.