It means they're the same size number, although they might not be both positives or both negatives. In other words, they are the same distance from zero.
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Yes, a positive integer and its negative have the same absolute value. For example, +5 and -5 have the same absolute value.
Yes.
They will be the same absolute value with opposite signs. They don't even have to be integers.
No.They must have the same numeral, but can have opposite signs. So, for example, the numbers 5 and -5 are clearly not the same, but the absolute value of either number is 5.
If the signs are the same, add the absolute values and keep the sign. If the signs are different, subtract the lesser absolute value from the greater absolute value and keep the sign of the number with the greater absolute value.