Great Integer Posts!

There were a lot of very good posts. Here are a few.

Monday, November 24, 2008

integer operations - Liz

so now...... lets start of with vocab!!

VOCAB
1. INTEGER~one of the positive or negative numbers 1, 2, 3, etc., or zero.
2. OPPISITE~a person or thing that is opposite or contrary.


Ok, now first i will explain how to do an integer operation using addition and subtraction


RULES FOR ADDITION! (VERY IMPORTANT)

1. IF THE SIGNS ARE THE SAME (-3+-4) THEN ADD AND KEEP THE SIGN OF BOTH NUMBERS.
EX. 2+3=5 -4+-5=-9

2.IF THE SIGNS ARE DIFFERENT (-4+2) THEN SUBTRACT AND KEEP THE SIGN OF THE BIGGER NUMBER.
EX. -70+83=13 3+-5=-2

Now that we have got that out of the way lets see some problems that we can do together.

so lets say we have 9+7=?
easy right? it equals 16
but what if we have -8+3=?
not so easy.....but just remember the rules ask yourself "what do i need to do if the signs are different" well all you need to do is subtract 8-3=5 right? yes! Then once you have subtracted all you need to do is add the sign to the bigger number to your answer,so your answer is -5

now its easy!!

ok that was addition now time for subtraction
now subtraction is a little bit harder that addition.

RULES FOR SUBTRACTION!! (VERY IMPORTANT)

1. CHANGE ALL SUBTRACTION TO ADDITION BY DOING PLUS THE OPPOSITE OF THE 2ND NUMBER.
EX. -3-7 WHICH NEEDS TO BE TURNED INTO -3+-7

did you get that??
i know its kind of confusing so, lets do some problems.

ok so lets say that we have 8--4.
so just remember the rules ask yourself "what do i need to change"
well you need to change subtraction to addition and do plus the opposite.(which means if you have -9 you change it to 9)
so now your changed problem should look like this 8+4
and then you just follow the rules if addition..... just add them together!!
so your answer is 12

now.... its time for...... multiplication and division and i swear this is the last thing.

RULES FOR MULTIPLICATION AND DIVISION!! (VERY IMPORTANT)

1. IF THE BOTH SYMBOLS ARE THE SAME THE ANSWER IS POSITIVE
2. IF THE SYMBOLS ARE DIFFERENT THE ANSWER IS NEGITIVE

So now lets do some problems.
so lets say you have -3x8=?
well the symbols are different so the answer is negitive.
but how you get the answer is you just multiply 8x3 and it is 24 but remember the answer has to be negitive so the answer is -24!!

ok so now division problems.
so lets say that you have -24 divided by 8
the symbols are different so the answer is negitive
now just divide 24 by 8 and you get 3
but remember your answer is negitive so the answer is -3

ok thats it!!! yeah!!
if your still having trouble check out this awesome site.

http://www.edhelper.com/integers.htm

then click on the thing that you still need help with!!

enjoy!!

Integers - Mia-pella

Integers - are a set of positives or negatives and their opposites (negatives or positives).

ex. 4 is a positive number. The opposite of positive 4 is negative 4 (-4). -5 opposite 5

note: 4 is bigger than -4.


Addition Rules

1. If the signs are the same (-3 + -4), then add the numbers and keep the sign of the numbers. -3 + -4 = -7 2 + 6 = 8 -5 + -9 = -14


2. If the signs are different ( -2 + 5), than subtract the small actual number (2) from the bigger actual number (5). Keep the sign of the bigger number (5). -2 + 5 = 3 -14 + 7 = -7

Subtraction Rule

1. Change the subtraction symbol to a plus then change the second number to it's opposite. -3 - 7 = -3 + -7 = -10 12 - 5 = 12 + -5 = 7 18 - -9 = 18 + +9 = 27


2. The two pencil mark rule - when you have an integer minus a negative you do two marks. You change the minus to a plus, then the negative sign to a plus. 17 - -8 = 17 + +8 = 25 -6 - -9 = -6 + +9 = 3

Subtraction really doesn't exsist! Any regular subtraction problem is really a number plus a negative.

Multiplication and Division

You think of multiplication as repeated addition.

1. 3 x 2 = 2 + 2 + 2 = 6 then 3 x -2 = -2 + -2 + -2 = -6


2. When the signs are the same ( 4 x 5 or -9 x -3), the answer is a positive ( 4 x 5 = 20 and -9 x -3 = 27).


3. When the signs are different ( 6 x -4 or -2 x 8), the answer is a negative ( 6 x -4 = -24 and -2 x 8 = -16).

It's the same rules for division.

Here's two sights that will help you learn, or if you just want to learn more: http://www.mathleague.com/help/integers/integers.htm http://www.math.com/school/subject1/lessons/S1U1L10GL.html

Here's something for practice: http://www.math-drills.com/integers.shtml

RayRayRocks!
Undoubtedly, Today I will teach you how to solve Integers! Integers are pretty easy, but there are a few different rules that might confuse you so I will have examples&vocab to help! I will teach you how to add, subtract, divide and multiply integers.

VOCAB!
Integer-the set of whole numbers and their opposites.

First-The easy one
-2+-3=-5 easy right?
As long as the signs are the same you just add get your answer and keep the same sign.

Now you get to the not so easy.
-2+3=1 might be a little confusing to you. but i will explain it.
Since the signs are different you subtract and keep the sign of the BIGGER number.

Now lets review.
1st. If you are adding and the signs are the same you just add and keep the same sign. 2nd. If you are adding and the sings are different you subtract and keep the BIGGER number.

Now lets move on to a little bit harder stuff -Subtraction.
-3--4- You might think that your subtracting here..and you are but something that might help is the 2 pencil mark which is when you make the minus sign a plus sign and you change negative 4 to postive 4. So your problem now is really -3+4 which is really 4 minus 3 = 1.

So lets move on to Multiplication.
First 2 very important things that you HAVE to know.
1st. when the signs are the SAME you keep the answer positive.
2nd. when the signs are DIFFERENT you make the answer negative.

-7x-3=21 notice how it is positive 21 because the signs are the same.
-7x3=-21 now the answer is negative 21 because the signs are different.


Finally, Divison!
Remember the rules for Multiplication? well their the same for Divison!

-27/-3=9 by the way / means divide=] your answer would be positvie 9 because the signs are the same.
-27/3=-9 It's negative 9 because the signs are different.

I hope if you didn't understand this before you do now!

Just remember a few things.....
addition-if the signs are the same you just add&keep the same sign. If the signs are different you subtract and keep the sign of the bigger number.
subtraction-when you subtract you do the "2 pencil mark" which is when it is subtraction you change the minus to a plus and if it is positive you make it negative and if it is negative you make it positive.
multiplication-If the signs are the SAME you just multiply and make the answer POSITIVE! and if the signs are DIFFERENT you multiply and make your answer NEGATIVE!
divison-same rules as multiplication...if the signs are the same-positvie and if they are different-negative and you just divide!

Just remember these few things and I think you'll be fine!

But if you don't understand integers and this didnt help you then go to this website..and I think it will help!

Positive and negative integers

Great Equation Posts!

The Below posts by Noah, Kelly, and Caitlin are WONDERFUL. Please take some time to read over them.

How to Solve Equations

The Fundamental Principles of Algebra

1. We are trying to get the variable by itself (isolating the variable).

2. Whatever you do to one side of the equal side you must do to the other side.

Steps For solving equations

1. Ask yourself what is being done to my variable.

2. Do the inverse operation to both sides of the equation.

3. Now, your variable should equal the answer.

Ex. 2+n=8 1. I am adding 2 to my variable.

-2 -2 2. I subtracted 2 from 2 and 8

n = 6 3. So, n = 6.

Checking Equations

1. Rewrite the problem. 2+n=8

2. Replace the variable with the answer. 2+6=8

3. Do all the operations to get your answer. 2+6=8

8=8

4. Your variable should equal the answer. n=6

Vocabulary

Equation: two numbers or expressions that are equal in value

Variable: any letter that can represent a number and can vary

Inverse Operations: operations that undo each other (do the opposite)

2 Step Algebra

1.What is being done to my variable? 2+ 7x=58

2. Make whatever number that is not with the variable a 0. -2 -2

3. Do inverse operations to the number next to the variable. 7x=56

7x/7=56/7

4.One times anything is itself. 1x=8

5. The variable should equal the answer. x=8

Extra Help

http://www.inmath.com/Basic-algebra/Basic-algebra-intro.php- this is a home page to many places where you can get help for algebra.

http://www.algebrahelp.com/lessons/equationbasics/index.htm-on this site look at pages 1-5.

Solving Algebraic Equations

Key Terms You Have to Know:

Variable: Something that is capable of being changed.

Fundamental Principles:

1.You're trying to get the variable by itself (Scientists call it "isolating the variable").

2. Whatever you do to one side of the equals sign you MUST do to the other side.

How to solve equations!

Step 1: Ask yourself: what is being done to my variable? (Ex. If you have n-4=8, you see that your variable is being subtracted by 4).

Step 2: Do the inverse (opposite) operation to both sides of the equation or both sides of the equals sign. (Ex. If we keep our same example n-4=8, then you ADD 4.) So far our problem would look like this:

n-4=8

+4 +4

WARNING: Do not do the same operation as the problem!

Step 3: Write variable = answer. (You need to know that in the problem -4 +4 = 0 so it just cancels out. So then when you add 8+4 you get 12, and you drag your variable down.)

The completed problem looks like this:

n-4=8

+4 +4

n=12

Always remember to line up your equals signs!

Now you know how to solve equations, but do you know if your answer is right? If you said no you're right. You do not know if your answer is right. You need to check it. But how? I'll tell you.

Step 1: Rewrite the problem (We'll keep n-4=8).

Step 2: Plug in your answer where the variable is ( Our variable is n, so we put our answer 12 where n is. That would create something that appears like this 12-4=8).

Here is where it gets confusing. You actually have to solve 12-4. It just so happens that the answer really is 8. But if you subtract you number (4) from your variable (n=12) and you don't get the same answer as before, then you know your answer wrong. In our case it's right so I will move on to step 3 of the check.

Step 3: If you know your answer is right then you write it=it, but not literally it. (Our number is 8, so you would write 8=8).

Our check would look like this so far:

n-4=8

12-4=8

8=8

Step 4: Write the variable and what it equals. (Ours would be n=12).

Our finished check would look like this:

n-4=8

12-4 =8

8=8

n=12

That's how you check!

Further explanation of the problem solving:

When you have a division problem and must multiply to get your answer, the problem is set up a little different. You will end up with only 2 lines instead of 3.

Example of how you solve these problems:

3*n/3=33*3

n=99

How did I solve that? Well, the problem is n/3=33. So you do the inverse operation: multiplication and 33*3= 99. There you have it! n=99!

Variable Help?

www.purplemath.com/modules/variable.htm

When will I ever need to use this? Well, I can tell you that accountants use this stuff almost everyday. At least I know my mom does. So, if you ever want to work for a bank or be an accountant be sure you know this stuff!

Goodbye!

Solving Equations

Are you wondering how to solve equations? Well you have came to the right place!

The vocabulary you need to know is variable and equation.

variable - it can be changed or varied.

equation - a statement of equality between two quantities , as shown by the equal sign(=)

How To Solve The Problem

Now here is a example of a equation 3 + q = 10

You need to ask your self what is being done to my variable?

What's being done to your variable is adding.

Now do the inverse operation (opposite) to both sides of the equation.

example 3 + q = 10 the opposite of adding is subtracting.

So now you need to do this 3 + q = 10

Underneath the 3 and 10 you need to put minus 3

example 3 - 3 which aculaty would just equal Q because 3 minus 3 would just equal 0.

But for the 10 you would do 10 - 3 which would equal 7.

So now that you have just the number 7 and Q you now do Q =7

Now you want to make sure you are fully right about the answer and you would need to check it.

First you need to rewrite the equation.

example 3 + q = 10

So now that you rewrote it you can plug the number that you got which was 7.

example 3 + 7 = 10

So does 3 = 7 = 10?

Well it does so that is when you know that you got the right answer!

The next step is to write that 10 = 10 and also that q = 7.

Now there are other equations like 4m = 20 and the inverse operation for that would be division. Now you just do the same thing I just showed but you need to do it in division not subtracting.

The other operation is division and it is a little bit different from the others because you do not write the number you are timing underneath the problem you would right it across from the equation.

example 4 x 12 = s/4 x 4

Real Life Application

So say you have 4 people and there is 20 goody bags and they all want five goody bags. So how would you do this? Will you have enough?

example 4m =20

Now you need to do 4m divided by 4 and 20 divided by 4.

example 4m divided = m and 20 divided by 4 = 5

Hey you have enough goody bags to each person 5!

Now you need to check it!

Once again you need to rewrite out your equation and plug in 5.

example 4 x 5 = 20

so 20 = 20 and m=5

.

Here is an awesome link to learn more about solving equations!

MathSteps: Grade 6: Linear Equations: What Is It?