What is the absolute value of each number below? 1. | -16 | = _ 2. | -xy | = 3. | 10 | = 4. | -0.9 | = _ 5. | -5 | =
The Correct Answer and Explanation is:
The absolute value of a number is defined as the distance between that number and zero on a number line, regardless of direction. This means that the absolute value of any positive number or zero is the number itself, and the absolute value of any negative number is its positive counterpart.
Let’s go through each of the examples:
- | -16 | = 16
The number -16 is a negative number. The absolute value of -16 is the distance between -16 and 0 on the number line. Since absolute value ignores the sign and only measures the magnitude, the absolute value of -16 is simply 16. - | -xy | = xy
Here, -xy represents a product of variables x and y, where the negative sign is attached to the product. The absolute value of -xy, just like with any negative number, is the positive version of that product. Therefore, the absolute value of -xy is xy, which assumes that both x and y are real numbers. - | 10 | = 10
Since 10 is already a positive number, its absolute value is simply the number itself. So, the absolute value of 10 is 10. - | -0.9 | = 0.9
The number -0.9 is negative. To find the absolute value, we remove the negative sign, so the absolute value of -0.9 is 0.9. - | -5 | = 5
The number -5 is a negative number. Its absolute value is 5, as we ignore the negative sign and just take the magnitude of the number.
In summary, the absolute value function eliminates any negative signs and provides the non-negative version of the number. This is why the absolute value of any negative number is positive, and the absolute value of any positive number or zero remains unchanged.
