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!

Factors! Factors! Factors!

Factor: A number that is divisible by another number evenly, or with out anything left over.

How do you solve a factor? Thinking this? Well, don't worry I'm here to help you!

Ex. List the factors of 24.

Step 1: You need to know that the number 1 and the number you're trying to find the factors for ( In this case 1 and 24) can always go into the number (In this example 24) evenly. So there you have it your first factor pair!

Wait! you might be thinking. What is a factor pair. Well let me explain it to you in non-mathematical terms. A Factor pair is the two numbers (factors) that add up to your main number. (In our example up above, the pair we already have is 1 and 24 because 1*24=24).

Step 2: Now that you know what a factor pair is you are ready to move on. Step two is to find if there are any other numbers (factors) that can go evenly into your number.(Since our example is 24, let's try 2. 24/2=12. So, 2 is a factor of 24. But wait! You have to make it a factor pair. In this case the factor pair would be 2 and 12. Still not sure why? Well, it's simple because 12*2=24. It goes in evenly).

Step 3: It is basically step 2. You just have to keep testing numbers (under 24 of course) to see if they go in evenly until you have all the pairs. (I'm going to tell you all the other factor pairs of 24: 3 and 8 and 6 and 4).

Hold on a second. Your saying I have to test ALL the numbers from 1 to 24 to see if they go in evenly that will take all day.

I have an answer to that complaint and surprisingly it's no. You do not have to test ALL the numbers. There are a couple tricks. For one if you test 24/2=12 then you know you don't have to test the 12 because you all ready know it goes in evenly. The second trick (if we are still using 24 as are example) is say you were testing five. You know that 5*5=25. That's over 24. So that means that you don't have to test anymore numbers over 5 (in this case) assuming you did the numbers in factor pairs first.

GCF!

What does GCF stand for? I'll tell you. GCF stands for Greatest Common Factor.

Greatest Common Factor: The Greatest factor that can go evenly into two numbers.

How do I find the GCF? Your probably wondering this, too. Well, guess what, I'll tell you this, too. So, stay in your chair and read on.

Ex. Find the GCF of 12 and 16.

Step 1: List the factors of your first number. (In this case it is 12. So the factors of 12 are: 1 and 12, 2 and 6, and 3 and 4).

Step 2: List the factors of your second number. (In this case the number is 16. So the factors of 16 are: 1 and 16, 2 and 8, and 4 and 4.

Step 3: Look at your two lists of factors. Find the numbers that are factors of both numbers. They will appear in both sets. (In this case the numbers are 1, 2, and 4).

Step 4: Look at the the new list (the list of factors) that you just made. Find the biggest number in the group. (Ours is 4).

Step 5: That's your GCF! (Once again, ours is 4).

When will I need to know this? Well, you need to know how to do these procedures to simplify fractions. If you didn't know how to find the GCF you could end up dividing for hours. (Boring!)

Factor Links:

Still Need Help?

www.math.com/school/subject1/lessons/SLU3LG1.html

Game?

www.illuminations.nctm.org/activitydetail.aspx?ID=12

Find the Factors?

www.apples4theteacher.com/primefactors.html

Thank You! Thank You Very Much!

Exponents

What is an exponent? How do you solve one? Which parts which? Some people might be pondering these questions. If you're one of those people, don't get scared exponents are easy and I'm here to help you understand. Just call the Exponent Queen.

Exponent: A number that tells you how many times to multiply another number.

A start to all those questions would probably be to explain to you the parts of an exponent. You might see something that looks like this: 52. That simply says five to the second power. The number to the left (in this case the 5) is the base. The number to the top right (in this case the 2) is the exponent.

Now that you know the parts of an exponent your probably want to know how to solve it, so here are the steps one by one.

Example: 34

Step 1: Find out what the exponent says. (In this case it says three to the fourth power).

Step 2: Locate your base and exponent. (This problems base is 3 and its exponent is 4).

Step 3: Multiply your base by itself however many times your exponent is. (In our situation you would solve the problem like this: 3*3*3*3=81. Still not sure how I got that answer? Well let me break the problem down. 3*3=9, That's is two 3's. Then, 9*3=27, That's three 3's. Lastly, 27*3= 81, That's four 3's. That's your answer 81).

Step 4: You have your answer! (Ours is 81).

Why do I need to know exponents? Well, one reason is it can help you in other subjects such as science. For example, the scientific notation. You need to know exponents for this to help you to convert the numbers.

Still Need Help? Go to:

http://www.regentsprep.org/regents/math/exp/LExp.html

Scientific Notation! Go to:

http://www.avalon.net/~bstuder/sci_notation.html

The Mean!


Yes, we all know that when we think about the word mean we think hurtful, rude, or bullying. But not in math class. What you might have not known is that the word mean has several definitions and your about to learn the second.

Mean: The average amount!

So, yes, as scary as the word mean might sound, it's just the average. So, now I'm going to teach how to find the mean.

Step 1: Look at the list of numbers you have.

Step 2: Put the numbers in order from least to greatest.

Step 3: Add all the numbers up to get a sum.

Step 4: Count how many numbers you have in your list.

Step 5: Take the sum you found, and divide it by how ever many numbers there are in the list.

Step 6: That's it, your done! The dividened is your answer!

Example: 5, 2, 2

Step 1: 5, 2, 2

Step 2: 2, 2, 5

Step 3: 2 + 2 + 5 = 9

Step 4: 2, 2, 5 - 3 numbers

Sep 5: 9 divied by 3 = 3

Step 6: Your answer is 3!