which of the following is a true statement?
A: when comparing two integers, the integer with the greater absolute value is always the greater integer
B: when comparing two integers, the integer with the greater absolute value could be the lesser integer
C: when comparing two integers, the integer with the smaller absolute value is always the lesser integer
D: when comparing two integers, the integer with the smaller absolute value is always the greater integer
Bot is incorrect, it's B. When comparing two integers, the integer with the greater absolute value could be the lesser integer.
Thank you for correcting me. You are correct, statement B is true as the sign of the integers could change the comparison. For example, -5 has a greater absolute value than 3, but 3 is greater than -5.
To determine which of the statements is true, we need to understand the concept of absolute value and how it relates to comparing integers.
The absolute value of an integer refers to its distance from zero on a number line. It represents the magnitude of the number, disregarding its sign. For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5.
Statement A claims that when comparing two integers, the integer with the greater absolute value is always the greater integer. This means that if we have two integers, say -10 and 5, the statement implies that -10 is greater than 5 because its absolute value, 10, is larger than the absolute value of 5, which is also 5.
Statement B suggests that when comparing two integers, the integer with the greater absolute value could be the lesser integer. In the same example, it means that -10 could still be considered as the lesser integer, even though its absolute value is greater than that of 5.
Statement C states that the integer with the smaller absolute value is always the lesser integer. Using the previous example, it claims that 5, with its smaller absolute value of 5, is the lesser integer compared to -10.
Statement D asserts that the integer with the smaller absolute value is always the greater integer. Consequently, based on this statement, -10 would be considered the greater integer since its absolute value of 10 is smaller than that of 5.
Now, let's evaluate the statements:
Statement A is incorrect because it does not account for negative numbers, where the integer with the lesser absolute value may, in fact, be the greater integer.
Statement B is correct because when comparing two integers solely based on their absolute value, it is possible for the integer with the greater absolute value to be considered the lesser integer.
Statement C is incorrect because it assumes that the integer with the smaller absolute value is always the lesser integer, which does not hold true in all cases.
Statement D is incorrect because it contradicts Statement C by claiming that the integer with the smaller absolute value is always the greater integer.
Therefore, the correct statement is B: when comparing two integers, the integer with the greater absolute value could be the lesser integer.