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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?

Great Factor posts!

Below are some wonderful posts from Francesca, CarCar, and taetae. Nice job ladies!

Factors

A factor is a number that can be divided evenly with 1 or more numbers.

12: 1, 12, 2, 6, 3, 4

1 x 12 = 12

2 x 6 = 12

3 x 4 = 12

The factors of 12 are 1, 12, 2, 6, 3, 4. Each pair of numbers multiplied together get 12. The way you do factors is take a number like 12. 1 abveously goes into 12 because 1 can go into any number above 0. Every number goes into itself. 1 x 12 = 12. Since 12 is an even number, 2 can go into it. But how many times? To figure it out, you go backwards. 12 divided by 2 is 6. 2 goes into 12 6 times. 2 x 6 = 12. You do the same thing to 3 and 4. It's easier if you start at 2 then work your way up.

Some tricks:

1. 2 if the number is even.
2. 3 if the sum of the digits are divisible by 3.
3. 5 if the number ends in 0 or 5.
4. 6 if the number is divisible by 2 and 3.
5. 9 if the sum of the digits are divisible by 9.
6. 10 if the number ends in o.
7. 11 (for 2 digit numbers) if the number is doubled.
8. 11 (for 3 digit numbers) if the two outside numbersadd up to the middle number.
   

When would you use factors? You use them when you have a party. How many candies go in each bag? I have 6 bags and 12 candies. 12 divided by 6 is 2. 2 and 6 are factors of 12. You would put 2 candies in each bag.

A great website for more practice is http://www.math.com/school/subject1/lessons/S1U3L1EX.html!!!!

Greatest Common Factor (GCF)

The Greatest Common Factor or GCF is the largest common factor of two or more numbers.

36: 1, 36, 2, 18, 3, 12, 4, 9, 6

48: 1, 48, 2, 24, 3, 16, 4, 12, 6, 8

The GCF would be 12 because 12 is the highest number they both have. The way you would do this is by listing the factors of each number. I look at the lowest number and it's factors. (36) Which ever factor is the highest number, I start there and work my way down. First, 36 can't go into 48. So, I move down to the next highest number. 18 can't go into 48 either. I go down again. 12 can go into 48. Maybe some of the lower numbers could go into it. But 12 is the highest one that can be divided by both numbers evenly. You would do the same with 3, 4, and maybe even 5 numbers. It's easier than you think.

Another website that would be good is http://www.helpwithfractions.com/greatest-common-factor.html!!!!

GOOD LUCK!!!!

taetae

Do you know what a factor Is? And do you know what the GCF mean's? Well If you don't know what those two thing's mean then I'm here to tell you!


First I will be talking about factor's and what they do&&what they are! Factor's
are number's that can be multiplied together to get another number. Which the other number is the factor. So now that you know a little bit about factor's let me give you three example's.


You can use your calculator for factor's!! Examples .Example A. Say you have 24, and you have to find the first factor's of that number.Well everyone know's 1*24=24 So 1 is a factor and the number itself 24. Then you go onto 2. So you think about what time's 2 give's me the answer 24? You use your calculator 24 divided by 2 and it =12.


Still don't get it? If you want some more information about factor's then go to this website&you can be a pro at doing factor's!
mathforum.org/dr.math/faq/faq.learn.factor.html (type in website)


Well Now that you know some information about factor's, and have a website to go to for practice your all set for a test&&quiz about factor's.

So now it's time to learn about the GCF!! You ready to learn about what the GCF mean's?? Well I know that I'm very excited to teach you!

First I'm gonna tell you what the GCF mean's, and what you do. Then I will give you some example's.


First Thing I will tell you, what the three letter's GCF stand for before we start anything else. It mean's Greatest Common Factor. Well now on to what you do when you have to find the Greatest common factor.


Greatest Common Factor mean's what number can be divided into both number's evenly. Then you pick the biggest number in both list and that's your GCF! Also It alway's has to be the same number. Because their trying to find this one very important number that can go into those two number's.


First thing you have to do is:

1. You have to list all the factor's of that number
2.Then pick which one is the biggest&&It has to be the same number that can be divided by both number's that they are asking for the GCF!
Those are the most two important thing's you have to do to find the GCF.

Now, I will give you two example's.

1. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54. So Which number can be divided into those two number's evenly? Remember It has to be the same number!

Answer: 18.
The reason why is because 36 can be divided into 18, and so can 54.

Need another example?? You Got it!

Example # 2: 12-1,12,2,6,3,4,4,3,6,2,12,2,
24-1,24,2,12,3,8,4,6,6,4,8,3,12,2


It's 12! Because, 12 can go evenly into both number's, also It's a factor for both number's.

So If you want a tiny bit more information so your a pro at It like you are in factor's now! Then go to this link, and get learning!

helpwithfractions.com/greatest-common-factor.html. (type in website)

Factor Poem's

I’ve been looking for divisors
Any way I can.
I want to find a pair of factors:
Multiplier, multiplicand.
Can’t you see this as a product?
Divided into parts.
You can even check your answer:
Multiply back to the start!

Factor ‘til you drop!
You’re not allowed to stop
‘Til farther you can’t go-oh-oh!
Factor all the time,
‘Til every factor’s prime;
Show us what you know!



CarCar

Factors and GCF

green=easy
yellow=medium
red=hard

Some people don't know what factors are and others don't know what the GCF is. If your one of them, don't be ashamed. I'm going to teach you what factors are and how to find the greatest common factor (GCF).

First, you have to know what a factor is.


Did you know that when you multiple a number by another number to get a product, those 2 numbers are called factors!
A prime number is a whole number greater than 1 that has exactly two factors 1 and itself.
A composite number is a number greater than 1 that has more than two whole- number factors.

Now that you know what a factor is it is time to move on to the GCF !

To find the GCF for two or more numbers you will have to find all the factors for each given number.

example:

24: 1,24 ; 2,12; 4,6; 3,8

36:1,36; 2,18; 3,12; 4,9; 6,6

48:1,48; 2,24; 3,16; 4,12; 6,8

The greastest common factor is the largest common factor of 2 or more given numbers.

Now that you know what a factor is and the GCF of a number is but before I'm done I want to teach you one more thing!



I will teach you least common multiple.

The smallest number , other than 0, that is a multiple of 2 or more given numbers.

example:

3:3,18,6,15,9,12

5:5,10,15,20,25

RED ALERT: DO NOT CONFUSE THE GREATEST COMMON FACTOR AND THE LEAST COMMON FACTOR!

Now guess what this is the easy part I've posted a web site for you to cheak out.

http://www.helpwithfractions.com/greatest-common-factor.html

Great Posts

The below posts by Caitlinishere, k-blog-kelley, and marielle101 are wonderful.

Exponents and Scientific Notation

You probably are wondering how to do exponents and scientific notation. Well, you are in the right place.

EXPONENTS
So say you have 2 to the 3rd power. The answer is 8. Now you probably are wondering how to solve that. So let me explain that to you.

ATTENTION: DO NOT DO 2 x 3 = 6.

This the right way to do it!

1. Find out what the base and exponent is.
   
   Example 2=base and 3=exponent
   
2. You need to think in your head what 2 multiplied 3 times is.
   
   Example 2 x 2 x 2
   
3. Solve the equation.
   
   Example 2 x 2 x 2 = 8
   
   

SCIENTIFIC NOTATION
Scientific notation is a way of writing a shorter version of a really big number. Here's an example.

The closest star to the Sun is the Alpha Centauri. It is 43,000,000,000,000 km away. When I write it in scientific notation which is 4.3 x 10 to the 13 power, it is much easier than to write it as 43,000,000,000,000.

Here's how I got the answer.

1. You always put the decimal point after the first number.
   
   Example 4.3
   
2. Then count how many decimal spots you move from the right until you get to the decimal point.
   
   Example For 43,000,000,000,000, I counted 13 spots.
   
3. Finally, you will write the number that you put the decimal point between then you would put down 10 to the 13 power.
   
   Example 4.3 x 10 to the 13 power

Down below is a link that you can look at to get more information about the scientific notation!

http://www.kidscosmos.org/kid-stuff/sci-note.html

K - Blog

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

Marielle101

If anyone ever asks you, what's two to the third power, and you have no idea what they are talking about, then you might want to read this. You can look at this well, whenever you want to, I guess, but especially when you need help or want to touch up on your math. I think the easiest way to teach exponents is to give an example and explain. Anyway, here goes:

In order to know scientific notation, you will have to know how to do exponents.

Here is your example: Four to the second power

If you have never done this before, you would probably guess 8. But that is not the correct answer. Four to the second power means that you multiply four by itself 2 times. In other words, it would be 4 times 4. That would give you answer of 16. For this problem, 4 would be the base, and 2 would be the exponent. The way I remember this is that the base is the bottom number, just like the base of a statue or microscope.
So, the big idea is that you are multiplying the base number by itself the number of times of the exponent.

• Why do you need to know this?

Well, exponents are used to take the place of really big or small numbers.

• Why is it called Scientific Notation?

The reason for this is exponents are often used in science. They are used for numbers such as the weight of a proton, or the speed of light.

That is basically all of what you should know about scientific notation and exponents. But, I also found a great site for this-

http://www.math.com/school/subject2/lessons/S2U2L2GL.html

This is a great website for more help that explains step by step, and in depth on how exponents work. Enjoy!

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Reflections

Our class will do reflections on what we learn in class. The posts that you make will demonstrate, solidify, and enhance your understanding of concepts while adding to the collective understanding of the class.

Below are some questions to help guide you in making quality posts.

1. What was today’s topic?
2. Explain in your own words how to do the topic?
3. What does the vocabulary really mean?
4. How might you use the topic in a real life situation?
5. Can you find any interesting links about the topic?
6. Can you relate the topic to something else we have studied this year?
7. Can you extend the topic to help us gain a deeper understanding?

In every post you should answer questions 1-3 and at last one from 4-7. In addition you need to respond to at least one of each of your classmates posts by the end of each term. I will collect some of the best posts and post them to my blog along with any resources I want to add. Your parents along with the world wide online community have access to the blog so that they can keep abreast of the class. Please respect your readers by making well-written quality posts.