The absolute value of any number is defined as the distance from zero to that number, without regard to the direction.
The size of a number itself is independent of the absolute value of the number. As positive numbers get larger, the absolute value of the number gets larger. As negative numbers get smaller, the absolute value of the number gets larger. The positive and negative values of any number have the same absolute value.
These properties of positive and negative numbers are illustrated on a number line. In the problems that follow, students are given two numbers and must determine which is the larger or smaller number and which has the larger or smaller absolute value.
The opposite of a number is defined as the number that has the same absolute value as the original number, but the opposite sign. If the original number is positive, the opposite is negative. If the original number is negative, the opposite is positive.
This is illustrated on a number line as a ray whose length represents the absolute value that is rotated about the zero point.
In the problems in this lesson, students are given positive and negative numbers and they must give the opposite of that number.