Question

If a and b are both negative numbers, and a > b, what must be true about their absolute values?

A) | a | = | b |
B) | a | > | b |
C) | a | < | b |
D) You cannot tell without knowing a and b.

Answer 1

If a and b are negative numbers with a > b, then | a | is less than | b | because a is closer to zero and thus less negative than b.

Step-by-step explanation:

If a and b are both negative numbers and a > b, then we must consider how absolute value affects these numbers. The absolute value of a number is a measure of its distance from zero on a number line, without considering the direction. Hence, the absolute value is always a non-negative number.

Since we are told a > b and both are negative, this means that in terms of distance from zero, a is closer to zero than b is. If we remove the negative sign by taking the absolute values, | a | would be less than | b |, because a is less negative than b. So the correct answer would be C) | a | < | b |.