Integer Operations

Integer operations seem confusing at first, but they're simple once you get the hang of it. Here is some vocab-



Integers- Both positive and negative counting numbers



Integer Operations- Equations using various integers



In order to perform these operations, there are also some rules you have to know. There are different rules for adding, subtracting, multiplying, and dividing.

Addition + Subtraction

1. When adding two integers with the same sign (negative or positive), you add the two numbers and keep the sign the same

1. -2+-9= -11

2. If you are adding and the signs are different, you add and keep the sign of the bigger number

1. -7+5=___

2. -7+5=-12

3. When subtracting, there's one rule- do plus the opposite. This means you want to make the subtraction sign an addition sign and put the opposite of the second number, like this:

1. 23-(-12)=____

2. 23+12=____

3. 23+12=35

Multiplication + Division

1. Anytime you are multiplying OR dividing two integers with the same sign, your answer will be positive

2. When you are multiplying/dividing two integers with different signs, your answer will be negative

---Caution!!!---

Be careful not to confuse you addition/subtraction rules with your multiplication/division rules!!!

NOTE:

THE PREVIOUS INFO COULD BE USED FOR MANY REAL LIFE SITUATIONS. EX- DOING BILLS OR DEALING WITH MONEY AND/OR DEBTS

For a complete do-it-yourself practice sheet, CLICK HERE

If you still need more help on solving problems with integers, CLICK HERE

If you want a repeat of the rules, CLICK HERE

If you want some integer games, CLICK HERE

Solving Equations

To somebody who has never solved an equation before, this seems rather difficult at first sight. To solve equaqations, you should probably know variables. Variables can be any letter that represents any number, changing. A quantity which may increase or decrease; a quantity which admits of an infinite number of values in the same expression; a variable quantity. I other words, a variable is any letter that can represent any number, and the number can change. In equations, you are trying to find out what the variable is representing in that problem. Or, another way to say it, you are trying to make both sides equal to find the variable. It is very important that whatever you do to one side, you have to do to the other. Here is how to solve one-


ex.
15+x=27

1. Write you problem/equation down on the first line.

2. Now, you might be able to just simply solve this in you're head, but since soliving an equation is a process, and solving equations mentally will not work when you move onto bigger problems, we won't. But, what we have to do now is subtract 15 from itself. But, we can't stop there. Whatever you do to one side you must do to the other. Like this-

15+x=27
-15 -15

As you probably already figured out, subtracting 15 from 15 is going to give you 0. This will always be you're 2nd step to solving you're problem. This is because you want to have the variable by itself.


3. On the next line you will have just you're variable and you're answer. It will look like this-

15+X=27
-15 -15
x=12

Now, you are done solving you're equation. Here is an example of how to do a equation with multiplication and/or division.

ex.

1. y divided by 12=5
2. 12 times y divided by 12=5 times 12
3. y= 60


ex.


1. 6 times y=54
2. divided by 6 divided by 6
3. y=9



That's how you solve equations!

Factors and GCF

Learing how to find factors is a pretty easy concept. A factor is a number that is divisible by another number. This means that a factor of any number will always be smaller than that number. In order to know the factors of any number, you will have to know the divisibility rules. Here they are-

2- If the number is even
3- If the sum of the digits is divisible by 3 ex.- 393... 3+9+3= 15 15 is divisible by three,
so so is 393.
4- If the last two digits are divisible by 4
5- If the last digit of the number ends in either 5 or 0
6- If the number is divisible by both 2 and 3
8- If the number formed by the last three digits is divisible by 8
9- If the sum of the digits is divisible by 9
10- If the number ends in a 0

Now that you the divisibility rules, I'll explain factors. You start with two, and go up to tean, finding if each number can be multiplied by anything to get the number. Here is an example:

The factors of 32 are:
1, 2, 4, 8, 16, 32

WORK:
32- 1, 32, 2, 16, 4, 8

NOTE:
1 is divisible by 32 because every number is divisible by itself and one (32 divided by1 is 32)

GCF:

When find a GCF, you have to be able to find factors. GCF stands for greatest common factor. That means, the highest factor that two or more numbers have in common. Here is an example of what to do:


Find the GCF of 25 and 30.

WORK: 25- 1, 25, 5
30- 1, 25, 2, 15, 3, 10, 5, 6

The GCF of 25 and 30 is 25, because out of the common factors, 25 is the biggest. This isn't the only way to do it, though. With more than two numbers, or with just two numbers, there is a shorter way. Here it is:

WORK: 25- 1, 25, 2, 15, 3, 10, 5, 6

Now, you would go down the list of factors, seeing if they are factors of 30 in your head. Then you would meantally figure out which one is the biggest/highest.

In real life, you might use this for making packages, or dividing things up. Hope you enjoyed my post!
Thanks for taking the time to read my post about factors
and GCFs. If you need more help, check out the
website below.


http://www.mathnstuff.com/math/spoken/here/1words/g/g3.htm

Picture

Something you should know about me is that I LOVE taking pictures, drawing, and searching the web. With pictures, the type of pictures that I take the most are probably nature and/or scenery pics. As a matter of act, I took this pic one evening in my neighbors yard. It's probably one of my favorites. I'll probably show you some more nature/scenery pictures another time. I think, when I grow up I'm going to be a part time photographer, and a school band teacher. So, enjoy the online scenery!

Hey! I guess you are probably wondering why in the world would i have a prom dress in my blog. Well, remember when I said I would talk about random stuff in my blog? Well, uh, ya, uh... very random.


What do you do when you are bored to death? Well, as you can see, I google image random stuff for no apparent reason!

Intro

Hey Guys! This is my blog, mariellie101. It's pretty sweet if you ask me! I was taught that a blog is where you just talk about random or non-random stuff! As, far as my writing goes... well, not that well. But talking? No Doubt!!! So I last night, I was thinking about what I would put in my blog... what time I went to bed last night? No way. Different bones of the human body? Hu-uh. When you think about like talkshows such as, for example, Ellen, people just like to hear random stuff. So, after that, I concluded that random stuff is what you will most likely enjoy reading. So, read on and enjoy my blog!!!

Oh, and please post some comments while your at it!! I like to hear from people!!!

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