you have a numeral that represents a negative integer, you can get the numeral representing its
absolute value by removing the minus sign.Meet the variables!
When you want to talk about how numbers relate to each other but don’t want to specify any
particular numbers, you can use variables instead. For variables representing integers, math-
ematicians most often use small, italic letters from a through q. When you see something
likea+b=c, you know you are supposed to add a quantity a to another quantity b to get a
third quantity c. You don’t have to know what the actual numbers are, but only that they are
related in a certain way. The term variable means that a quantity doesn’t have any fixed value;
it can vary.To add, move upward
Now let’s get back to displacement. We’ll go up and down here, because we’ve already illus-
trated the number line in a vertical sense. Think of upward distances as positive displace-
ments, and downward distances as negative displacements. If we have an integer a and we
want to add another integer b to it, we first find the point on the number line representing a.
Then we move up b units. That will get us to the point representing a+b.
As an example, suppose a=−3 and b= 2. We start at the point for −3 and move up 2 units.
That gets us to the point for − 3 + 2. It happens to be −1, as shown on the left side of Fig. 4-2.52 Addition and Subtraction
012312- 3
|2| = 2|-3| = 3
Figure 4-1 The absolute value of a number is its distance from 0 along
the number line. The direction (up or down, positive or
negative) doesn’t matter. That is why absolute values can
never be negative.