Final answer:
The term 'opposite' relates to numbers or directions that are reverse to a reference point, while 'absolute values' represent the distance from zero on a number line and are always non-negative. Opposites are about directional change, whereas absolute values quantify magnitude without direction.
Step-by-step explanation:
The difference between opposite and absolute values in mathematics lies in their distinct concepts. The term 'opposite' typically refers to numbers or directions that are in reverse relative to a certain reference point or direction. For example, if the chosen positive direction is to the right, then the opposite direction would be to the left. When discussing numbers, the opposite of a number is what you would add to that number to get zero; for instance, the opposite of +3 is -3, and vice versa.
On the other hand, the absolute value of a number is defined as the non-negative value of that number without regard to its sign. It represents the distance of that number from zero on a number line. For example, both +3 and -3 have the same absolute value of 3, because they are both three units away from zero on the number line. The absolute value is often denoted by two vertical bars; for example, the absolute value of -3 is written as | -3 |, which equals 3.
In summary, while 'opposite' involves directionality and refers to a number that would yield zero when added to the original number, 'absolute values' speak about magnitude without considering the direction, thus always a positive number or zero.