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Integers: Integers are whole numbers (as compared to decimal numbers or fractions). They can be positive or negative. How can you have a negative number, you ask? Until you accept and become used to working with negative numbers, the concept may sound a little strange. Think of it this way, though: Assume that the bank where you have your account is unwise enough to extend an overdraft (in other words, the bank will give you a credit line - in effect a loan). If you spend all the money you have had in the account and then you write another cheque for $100.00, with your account at a zero balance, the next bank statement you will receive in the mail will show a balance of -$100.00. That means that you owe the bank $100.00. (Our job here is to explain math, but we would like to make certain that you understand how we feel about borrowing money: DON'T!!!) What happens, when you subtract a number from a negative number?
The above expression can also be written as
When subtracting a number from (or adding a negative number to- same thing) a negative number, you will add the two together and the result will have a negative sign. Let us use our example of a bank account with a balance of -$100.00. What happens (given that your credit line is sufficient), if you write another cheque for $100.00 drawn on the same account?
Your account had a balance of -$100.00 to begin with and you have written another cheque for $100.00, so that your balance of what you owe your bank will change to -$200.00. What happens, when you add a positive number to a negative number?
When you are adding a positive number to a negative number, you subtract the lower number from the higher number. The result will have a positive sign, if the positive number you are adding has a higher numerical value than the negative number and it will have a negative sign, if the negative number that you are adding to has a higher numerical value than the number you are adding. If both number are the same, the result will be 0. To return to our bank example, with your account at -$200.00, if you will make a deposit of $100.00, you will owe the bank only -$100.00:
If your deposit will be $200.00, your account will have a 0 balance following the deposit:
If you deposit $500.00, you account will have a balance of $300.00:
When adding or subtracting positive and negative numbers, the signs can be a little misleading. Our method will make it simple. Take a look at the following examples:
Take a look at the two signs above marked in red. The rule for adding/subtracting positive and negative numbers is:
In other words if you have two positive signs, you will add the numbers. If you have one positive and one negative sign (in any order), you will subtract the second number from the first number. If you have two negative signs, you will add the numbers. Use the following technique: First of all, do not try to do the calculation in your head. Not for a long time, until you are very certain of what you are doing. On a sheet of paper, write the expression in three parts: First, copy the first number exactly as you see it, including the sign before it, if there is one. For our first example, you will write down
Second, take a look at the two signs that follow the first number. In our first example we have a plus and a minus. Taking a look at our signs rule will tell us that a plus, followed by a minus means that the second number should be subtracted from the first, so that the next thing we will write will be
The third step in our technique will have you write down the second number WITHOUT THE SIGN - JUST THE NUMBER and you will write:
Our expression has therefore become simplified to:
Following the above method, you will never add instead of subtracting or vice versa. Now work on the following for practice: Strangely enough, multiplying and dividing positive and negative numbers is much simpler than addition and subtraction. Multiplying or dividing - two positive numbers will always give positive result. - a positive number by negative number (or a negative number by positive) will always give a negative result. - two negative numbers will always give a positive result. Examples:
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