Adding and Subtracting Signed Numbers
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 well 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. Lets see what that looks like on a number line.
How about adding two negatives? Well 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:
Easy, isnt it?
Adding numbers whose signs differ
This isnt so very hard either. On a number line, lets add 6 and 4.
We can see that 6+(4)=2. Do you think 4+6 should be the same? Lets 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 $2 balance.
I think its time for you to try these!
If you got these right, then you must have the idea. Now you are ready to learn subtraction.
Subtraction of Signed Numbers
Picture this on a number line: 73 =4
How about this one: -45=-9
You might note from these two examples that we get the same result for 73
as we do for 7+(-3) and similarly
-45 is the same as -4+(-5). The fact of the matter is, we really dont need a separate set of rules for subtraction. We just need to remember to add the opposite of the subtracted number. This isnt so far fetched.
Consider the hole-dirt-pile way of thinking. When you add a hole (a negative), it is just like subtracting a dirt-pile (a positive). If you subtract a dirt-pile (a positive), its just like adding a hole (a negative).
In a checking account, deposits are positive numbers and checks are negative numbers. If we want to remove a deposit of 5$ (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).
subtract a positive èadd a negative
subtract a negativeèadd a positive
subtract a number èadd its opposite
The rule for subtraction of signed numbers is that simple: we dont subtract, we add the opposite.
You should try these!
|9) -6(-10) = -6 +||=|
|10) 4(-8)= 4 +||=|
|11) -38 = -3+||=|
|12) 522 = 5+||=|
Now here is a list of mixed addition and subtraction problems you can practice on:
|15) -6 (-17)=|
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?