Integers & Solving Equations with Integers!

Key Terms You Should Know:

1. Integer - Any positive or negative whole number

2. Opposite - The exact difference of something

How To Solve Integer Equations - Addition!

Rules To Know when adding Integers:

1. If the signs are the same add and keep the sign.

2. If the signs are different subtract and keep the sign of the bigger number

Examples:

Step 1: Look at your problem. Are your signs the same or different? (Ex. We are going to use the problem -2+-2. The signs are the same.

Step 2 (If the signs are the same): Add your two numbers together. (Ex. Since our problem is -2+-2 you would add 2+2 and get 4.

Step 3 (If the signs are the same): Keep the sign and you are done! (Ex. Since 2+2= 4 and both of the 2's are negative you keep the negative sign. You get a finished problem that looks like this: -2+ -2= -4.)

Step 1: Look at your problem. Are your signs the same or different? (Ex. We are going to use the problem -8+4. The signs are different.

Step 2 (If the signs are different): Subtract. (Ex. Since our problem is -8+4 you would subtract 8-4 to get 4.

Step 3 (If the signs are different): Keep the sign of the bigger number and you are done! (Ex. Since -8+4=4 and 8 is a bigger number than 4, you would keep the sign of the 8. The sign of the 8 is -. You get a finished problem that looks like this: -8+4=-4.)

How to solve Integer Equations - Subtraction!

Rules to know when subtracting Integers:

1. You must change the problem to addition.

2. You must change the 2nd number to its opposite.

Example:

Step 1: Look at your problem. (Ex. Ours is going to be -9-5.)

Step 2: Change the problem to addition and the 2nd number to its opposite. (Ex. Since our problem is -9-5 you'd want to change it to something that looks like this:

-9+-5.)

Step 3: Now, you follow the rules for addition. (Ex. Since our new problem is -9+-5 the signs are the same and you must add the numbers together and keep the sign. Our problem looks like this: -9+-5= -14.

Step 4 (optional): You can rewrite your original problem with the answer you found. (Ex. If you choose to do this step, it would look like -9-5= -14.)

How to solve Integer Equations - Multiplication and Division!

Rules to know when multiplying and dividing integers:

Please note that the main RULE for multiplication and division is the same.

1. Two numbers with the same sign always make a positive number.

2. Two numbers with different signs always make a negative.

Examples:

Step 1: Look at your problem. Is it a multiplication or division problem? (Ex. For this example our problem is going to be multiplication. The problem is -9*-5. Since both the numbers are negatives we already know that our answer is going to be positive.)

Step 2 (If the signs are the same): Multiply and get a positive. (Ex. 9*5 is 45. Since both signs are negative you get a positive 45.)

Step 3: That's your answer! (Ex. -9*-5= 45)

Step 1: Look at your problem. Is it a multiplication or division problem? (Ex. For this example our problem is going to be division. The problem is -6/3. Since one number is negative and the other is positive then we already know that our answer will be negative.)

Step 2 (If the signs are different): Divide and get a negative. (Ex. 6/3 is 2. Since the signs are different you get a negative 2.)

Step 3: That's your answer! (Ex. -6/3= -2)

When will I actually need to know this?

Say you are in debt. (Hopefully not, but it's just an example.) You would have to use negative and positive numbers to find out much you have in debt and how much you owe.

Still need Help?

Go to: http://www.mathleague.com/help/integers.htm

Goodbye!