Addition and Negative Numbers

If you add a negative number to a positive number, simply take the negative number away from the positive number. If the negative number is larger than the positive number, Take the positive number away from the negative number as if both numbers were positive, then put a minus sign in front of your answer. If you add 2 negative numbers together add them as though they are positive and put a minus sign in front of their sum. Lets look at 5+(-8)=? I show the same problem written several ways below.

The first way it is written is the way it's displayed in Homemade Math's exercises. Note that if we see a number and it doesn't have a plus or minus sign in front of it, it is assumed to be positive.

Using the number line, start at 5 on the right side of the 0 or origin, count 8 graduations to the left or in the negative direction, landing on -3. When we combine numbers on the number line, we move right or in a positive direction when they are positive numbers and move left or in a negative direction when the number is negative. Try -5+(-6)=. Start on the -5 count 6 more graduations to the left, landing on -11. Try -3+7=. Start at -3, count 7 graduations to the right or in the positive direction, landing on 4. Take a look at 6-3=? We are asking; what is the difference between 6 and 3 and not asking what the difference is between 6 and -3, which would be written 6--3=9. Count the graduations between these two points on the number line. Ponder this for a while as it is a source of confusion to lots of people. Back in Subtraction and Negative Numbers I mention that one way you end up with a negative number is to take a larger value away from a smaller value like in the problem 3-7=-4. Another way this happens is by our assignment. Say we have an air pressure tank and the pressure in the tank is the same as the air we are standing in. If we open the valve on the tank no air will go in the tank or come out because it is at the same pressure as our air. We can assign 0 P.S.I. to the pressure gauge reading when the air pressure in the tank is at the same pressure as the air around us. P.S.I. is an abbreviation for pound per square inch which is just a measure of pressure. Now if we pump the air pressure in the tank up to 10 P.S.I. we have +10 P.S.I. If we open the valve on the tank air will flow out until the pressure in the tank is equal to the pressure of the air around us which we have assigned to be 0 for convenience. We can also pump air out of the tank and make the air pressure in the tank less than in the air we are in. Say we pump air out of the tank until we reach -20 P.S.I. In this case we have a negative air pressure and if we open the valve on the pressure tank, air would rush into it until its pressure reaches the same value as our air pressure which we arbitrarily marked as 0. We are using the assignment of + and - to show weather air is going into the tank or being removed. We assign + and - values to all kinds of things. Savings accounts for saving money. When we put some money in the account we make it a + value to show its direction is moving into the account. If we take some money out of the account, we assign a - value to it to show it is moving out of the account.