54 Addition and Subtraction
Boulevard to be displaced by −4 miles. This means the jam has been displaced to the east
by 4 miles. The jam has moved in the opposite direction from the flow of traffic!
Look again at the right-hand side of Fig. 4-2. You add a negative number to some other
quantity. Adding a negative number is the same thing as subtracting the absolute value of that
number. Using variables, you can write that statement asa+ (−b)=a− |−b|which means the same thing asa+ (−b)=a−bIf you have an integer a and you want to subtract another integer b from it, first find the
point on the number line representing a. Then travel down b units. That will get you to the
point representing a−b.Are you confused?
Have you been wondering why negative numbers always have a minus sign in front of them, but positive
numbers don’t have a plus sign? Is there something technically wrong with including a plus sign so people
know when a number is positive? Why leave any doubt?
That’s a good question. The answer is that there’s no need for a plus sign in a positive number. A num-
ber is always assumed to be positive unless there’s a minus sign in front of it to indicate that it’s negative.
It is a mathematical convention. (In this context, “convention” means “custom” or “way of doing things,”
and not “a huge gathering of people.”) If you think about this for a little while, it makes sense. Why write
+ 3 + (+7) when you can write 3 + 7?Here’s a challenge!
In terms of the integer line, express the fact that when you subtract −5 from −3, you get 2. Write it down
in the simplest possible form.Solution
When you subtract a negative number, you move negatively downward, meaning that you actually travel
upward. Figure 4-3 is a number-line drawing that shows how this works. You start at −3 and move down
−5 units, which means you really move up 5 units. You finish at the point corresponding to 2. You can
write− 3 − (−5)= 2In its simplest possible form, this fact is written− 3 + 5 = 2