When do two numbers have the same absolute value?(1 point)
Responses
when both numbers are negative
when both numbers are negative
when the product of the two numbers is 1
when the product of the two numbers is 1
when they are opposites
when they are opposites
when one of the numbers is 0
when one of the numbers is 0
The two numbers have the same absolute value when they are opposites.
To determine when two numbers have the same absolute value, we need to understand what absolute value means. The absolute value of a number is its distance from zero on the number line, regardless of whether the number is positive or negative.
Now, let's go through the given options to find the correct answer:
1. "When both numbers are negative" - This answer is incorrect because the absolute value of a negative number is always positive. So, two negative numbers will have different absolute values.
2. "When the product of the two numbers is 1" - This answer is also incorrect because the product of two numbers being 1 does not guarantee that they will have the same absolute value. For example, the numbers -1 and -1 have a product of 1, but their absolute values are different.
3. "When they are opposites" - This answer is correct. Opposite numbers have the same absolute value. For example, -5 and 5 have the same absolute value of 5.
4. "When one of the numbers is 0" - This answer is incorrect because the absolute value of 0 is 0, but any non-zero number will have a non-zero absolute value.
Therefore, the correct answer is: "when two numbers are opposites."