In the last lesson, you learned about positive and negative numbers. In this lesson, we will learn how to add and subtract them. At first we’ll use a number line, then try some without it after we get some rules. I hope you remember the number line from the last lesson. Here is a picture of part of it:

Adding numbers of the same sign

Everybody knows 2+3 = 5. Let’s see what that looks like on a number line.

How about adding two negatives? We’ll look at a picture of -4+(–6).

If your checking account is overdrawn \$4 and you write a check for \$6, your checking account is then overdrawn by \$10. When you add a negative number to a negative number, you add the numbers and keep the – sign, so –4+(–6)= –10. Another way you can think of this is to think of playing in a pile of dirt. Negative numbers are holes, and positive nymbers are piles. If we dig a 6 foot hole in the bottom of a 4 foot hole, we would have a 10 foot hole, so –4+(–6)= –10. If we put a 3 foot pile on top of a 2 foot pile, we have a 5 foot pile, so 2+3 = 5. Test yourself on these examples:
 1) 4+5= 2) –3+(–4)=

Easy, isn’t it?

This isn’t so very hard either. On a number line, let’s add 6 and –4.

We can see that 6+(–4)=2. Do you think –4+6 should be the same? Let’s look at it on a number line.

Using the "playing in the dirt" idea, if we have a 4 foot hole and fill it with a 6 foot pile of dirt, we would have a 2 foot pile of dirt, so –4+6=2 as the picture shows.

If we have a 6 foot dirt pile and dig a 4 foot hole in it, we are 2 feet above ground level, so 6+(–4)=2.

Similarly, if we have a checking account that is overdrawn by \$4 and make a \$6 deposit, we would have a \$2 balance. If we had a \$6 balance and wrote a \$4 check, we would have a \$2 balance.

I think it’s time for you to try these!
 3) 7+(-3)= 4) -9+2= 5) -5+1= 6) 1+(-5)= 7) -15+7= 8) 8+(-20)=

If you got these right, then you must have the idea. Now you are ready to learn subtraction.

Subtraction of Signed Numbers

Picture this on a number line: 7–3 =4

You might note from these two examples that we get the same result for 7–3 as we do for 7+(-3) and similarly
-4–5 is the same as -4+(-5). The fact of the matter is, we really don’t need a separate set of rules for subtraction. We just need to remember to add the opposite of the subtracted number. This isn’t so far fetched.

Consider the hole-dirt-pile way of thinking. When you add a hole (a negative), it is just like subtracting a dirt-pile (a positive). If you subtract a dirt-pile (a positive), it’s just like adding a hole (a negative).

In a checking account, deposits are positive numbers and checks are negative numbers. If we want to remove a deposit of 5\$ (subtract a positive) it has the same effect as adding a check for \$5 (add a negative). On the other hand if we wish to remove a \$10 check from our records (subtract a negative), we wind up doing the same thing as if we added a \$10 deposit (add a positive).

Review:

subtract a positive èadd a negative

subtract a number èadd its opposite

The rule for subtraction of signed numbers is that simple: we don’t subtract, we add the opposite.

Therefore 7(-3)=7+3=10

and -97=-9+(-7)=-16.

You should try these!
 9) -6–(-10) = -6 + = 10) 4–(-8)= 4 + = 11) -3–8 = -3+ = 12) 5–22 = 5+ =

Now here is a list of mixed addition and subtraction problems you can practice on:
 13) -7+5= 14) 7+(-11)= 15) -6– (-17)= 16) 22–(-12)= 17) -14–5=

18) On January 15, the high temperature in Honolulu, Hawaii was 79 degrees while the high in Nome, Alaska was -18 degrees. How many degrees warmer was it in Honolulu?

19) The highest land point in California is Mount Whitney, with a height of 14494 feet above sea level. The lowest point in California is Death Valley with a height of 287 feet below sea level. What is the difference in their heights? (Don't use a comma!)

20) If you have overdrawn your checking account by \$75, make a \$50 deposit and write a check for \$15, what is your new balance?