Question

The difference of two negative integers is not necessarily negative.
True
False

Answer 1

The difference of two negative integers can indeed be positive. When subtracting a larger negative number from a smaller negative number, the result turns out to be positive, because subtraction of a negative number is the same as addition.

Step-by-step explanation:

The statement that the difference of two negative integers is not necessarily negative is true. Let's consider two negative integers,
`-4` and
`-6`. If we are to find the difference by subtracting
`-6` from
`-4`, we change the sign of
`-6` to plus because of the subtraction operation (as subtraction is equivalent to adding the opposite number). According to the rules of addition and subtraction involving negative numbers:

• For two negative numbers, we add their absolute values and keep the negative sign. For example,
  `-4 + (-2) = -6`.
• However, when subtracting one negative number from another, we actually add their absolute values, but since the larger absolute value has the negative sign, the result may be positive. For instance, subtracting
  `-6` from
  `-4` results in
  `-4 - (-6)`, which is the same as
  `-4 + 6`. This equals
  `+2` thus giving us a positive difference.

Therefore, the difference between two negative numbers can in fact be positive if the number being subtracted has a larger absolute value.