Adding Integers

Adding integers

We are going to start with the method used for when we have the same sign.


Same sign: This is the simple part of adding integers, when adding with the same sign you pretty much just add it. When you add with negative sign just pretend the sign isn't there and just put them in at the end, like so. But for adding it's just adding them both together.

Example:    Beginning: (8) + (6) = (14)
             End: (-8) + (-6) = (-14)

                    (+6) + (+6) = (+12)

Different signs: When adding with different sign you use the sign with the biggest number, so if you have (+6) + (-3), you have to use the sign with the larger number in this case it's +.

Example:    (+8) + (-3) = (+5)
                 

This is it for my blog i'm sorry it's not to long because I lost my notes, but I tried my best and i'm going to make a better adding integers blog this weekend.

Subtracting Integers, YEAH

Subtracting Integers
Anian here. Subtracting Integers? Oh.
1. This could start in different ways, either (-N) - (-N) , (+N) - (+N) , (-N) - (+N) or (+N) - (-N).
N=any number
Examples: (-5) - (-2) , (+6) - (+4), (+5) - (-4) and (-9) - (+7).
2. Now let's really start now,

(-5) - (-2) = (-3)
- - - (- -)->
(-3)
This is pretty much the math that we are all use to. How do I know? Well, notice the negative sign/symbols, they're the same. Here is a tip: if you want you can ignore the symbols completely, then afterwards put back the symbols. This only works if both integer have similar symbols.

(+6) - (+4) =  (+2)

+ + (+ + + +) ->
(+2)
Almost the same as before, the only difference is that this is positive. The one before was negative.
NEXT!

3. Now things get interesting,

(+5) - (-4) =

+ + + + + Wait, how do you take away (-4) out of (+5)? Zero pairs! I'll show you.

+ + + + + + + + +
 (+9)       ( -  -  -  - )->

By adding  a few zero pairs, doesn't change the integer. Now you can take the negative or positive. If you add any extra won't make any difference as I said before, zero pairs doesn't change the integer.

(-9) - (+7) =

-  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -
(-16)                   ( + + + + + + + )->

Same as before, except vice versa. Just read the one before.
Very AWESOME AMZING TIP:
Take a look at (-9) - (+7). Now look at (-9) + (-7). If you notice, they both equal (-16). Here is the tip, do the opposite or make them the same symbol, then the opposite of the equation symbol, that is either plus or minus.


Now, I hope that I helped. And thank you for  taking a few minutes on reading this. Subtracting Integers, COMPLETED!

Adding & Subtracting Fractions With Like Denominators 

Adding Fractions With Like Denominators:

1) The first thing that you have to keep in mind is that when you are adding fractions with like denominators (the bottom numbers to your question) both denominators to your question are equivalent (the same).

2) Your second step is to focus on your numerators (the top numbers to your question) because if your denominators are equivalent then in the end the denominators will stay the same, so what you have to focus on when you are adding fractions with like denominators is your numerator because they are not equal. ex. ( 7/12+4/12) both numerators are not equivalent but your denominators are.

3) Now your last step is to add your numerators while your denominators are equivalent already so they stay the same:    7/12 + 4/12 = ?

                          numerators: 7 & 4   denominators: 12 & 12 

all you have to do since the denominators are the same is to add the numerators so 7 + 4 = 11 

and your denominator is 12 so your answer is   11/12

7/12 + 4/12 = 11/12 

Subtracting Fractions With Like Denominators:

1) You also have to remember that your denominators are the same so they will not be changed.

2) Your only difference is that you are subtracting your numerators and not adding them, so in the end your answer will be different. 

3) So your last step is going to change: 7/12 - 4/12 = ?

                           numerators: 7 & 4   denominators 12 & 12

all you have to do in this situation now is subtract the numerators instead of adding them so 7 - 4 = 3 and your denominator stays the same which is 12 so your answer becomes 3/12

                                                                 7/12 - 4/12 = 3/12

Now you know how to add and subtract fractions with like denominators!

Try These:

 

Adding:                              Subtracting:

1) 2/5 + 3/5                           1) 3/6 - 1/6

2) 10/20 + 8/20                     2) 7/15 - 2/15

3) 4/10 + 1/10                       3) 9/20 - 8/20 

 

Adding and Subtracting With Like Denominators

Water we doing?Wondering how to add or subtract fractions, like 5/8+1/8? Well, you came to the right place to somehow learn it.

ADDITION:
Notice that the denominators are the same, which means they are both cut into 8 equal pieces.Got that out of the way, STEP 1, COMPLETED!
Now, add the numerators to each other. Don't do anything with the denominator, because if you do anything with it. you are changing how the whole is cut into. STEP 2, COMPLETED!
If you feel that your answer is not at lowest term, well turn them into lowest term! To do that find a common multiple for them, then divide them by their common multiple. I suggest using the highest common multiple. STEP 2.5, COMPLETED!
THE MATH:

5/8+1/8=?      12=12      5+1=6      5/8+1/8=6/8    6/8- NOT LOWEST TERM
MULTIPLES OF 6-1,2,3,6
MULTIPLES OF 8-1,2,4,8
6/8 * 2/2= 3/4
*- DIVIDE
5/8+1/8=3/4

SUBTRACTION
Different numbers: 9/12-3/12
Again, notice that the denominators are again the same. That is kind of the point of adding and subtracting fractions with LIKE denominators. Well, the denominator are both 12, which means they are both equally divide into 12 pieces. Again, STEP 1, COMPLETED.
Now, subtract the numerator to each other. Again, don't do anything with the denominators, because it will mess up how much the whole is cut into. STEP 2,COMPLETED.
Again, if you think the answer is not at lowest terms, put it into lowest term, by finding the highest common multiple, then divide them by their highest common multiple. STEP 2.5, COMPLETED.
THE MATH:

9/12-3/12=?     12=12    9-3=6       9/12-3/12=6/12     6/12- ALSO NOT LOWEST TERM
MULTIPLES OF 9-1,3,9
MULTIPLES OF 3-1,3
6/12*3/3=2/4- STILL NOT LOWEST TERM 2/4*2/2=1/2
*-DIVIDE
9/12-3/12=1/2

NOW YOU KNOW HOW TO ADD AND SUBTRACT FRACTIONS WITH LIKE DENOMINATORS. NOW YOU CAN SHOW OFF TO YOUR FRIENDS WHAT YOU CAN DO!

Adding with like denominators: 
Your fraction addition statement is: 3\6 + 2\6
1) Look at the numerators and only focus on them for now. You are doing this because the denominator is the same and you don't need to work on it (both fractions have the same amount of equal parts in the whole and so will the answer)
2) Add the numerators
3) Your new number is your new numerator for the sum of this fraction statement
4) Your last step is to place your denominator back in the sum.
5) That's how you add with the same denominators :)

Subtracting with like denominators:
You will do the same steps as "adding with like denominators". The only difference is that you'll be subtracting the numerators, not adding it.
Your fraction addition statement is: 3\6 - 2\6
1) Look at the numerators and only focus on them for now. You are doing this because the denominator is the same and you don't need to work on it (both fractions have the same amount of equal parts in the whole and so will the answer)
2) Subtract the numerators
3) Your new number is your new numerator for the answer of this fraction statement
4) your last step is to place your denominator back in the answer
5) That's how you subtract with the same denominators :)

TRY THESE!!

1) 8/10-5/8              4) 9/9-7/9 

2) 3/7+3/7               5) 6/12-5/12

3)1/6+5/6                6) 12/25+9/25