Lizley's Scribe Post

Adding Integers

ex.
(+5) + (-2) = ?

How to add Integers:

1. Add these to help you out:
+5 = have 5
-2 = owe 2

2. +5 = +++++
     -2 = --

*The rest is 3 +'s. So the answer is +3

(+5) + (-2) = +3

ex.
(+6) + (-4) = +2
have 6  &   owe 4  = have 2
++++++
- - - -

Subtracting Integers

ex.
5 - 2 = +3
have 5 remove owe 2 = have 3

so it becomes..
5(-2) = +3

then use +s & -s

5(-2) = +3
+++++
--

Jacob's Multiplying Integers Scribe Post

Multiplying Integers-

3x4=12 

Repeated Addition: 4+4+4=12

Three groups of four

3x(-4)=                           (-2)x(+3)= -6

(-4)+(-4)+(-4)=12      / \   Remove 2 groups of +3      / \

3 groups of (-4)         |____(+++) (+++) _____________|

(----) (----) (----)                    ---     ---

(  )= groups    

                             (-2)x(-3)=+6

                             Remove 2 groups of -3

                       /\      +++  +++       /\

                        |____(---)  (---)_____|

(-2)x(+3)= removing groups        (+2)x(+3)= make groups

(-2)x(-3)= removing groups         (+2)x(-3)= make groups

Lotte's Integers Scribe

:)

LJ's Integer Scribe Post

  LJ's Integer Scribe Post

on January 6 ,2014 we learned how to add Integers

Integers are positive whole numbers, zero, and negative whole numbers that can be added or subtracted to each other. There are two ways to model an Integer question one way is to use integer chips and another way is to use number lines.

Integer Chips

(-5) + (+4) = (-1)

owe 5 and have 4 = owe 1

to use Integer Chips you must use plus signs (+) and minus signs (-) to represent positive or negative numbers and put them in this order. 

_ _ _ _ _

+ + + +   

each pairs have to be removed because (-1) + (+1) is equal to zero, which is why they are called Zero Pairs. The remaining signs is/are the answer.

       

Number Lines

(-5) + (+4) = (-1)
owe 5 and have 4 = owe 1

to use Number Lines you must use arrows and Integers to represent the solution, like this.

     +4 ---->| -1                                    
          <----- +5                         
__________-0+__________

Rafael's Integer Scribe Post

Integers

Figuring out integers is pretty easy. Here let me show you.

Example:

No.'s are +5, and -6

(+5)+(-6)= -1

There you go, see how easy it is.

But that's not the only things you need.

You may also use two proper visuals to represent your answer like:

Now we are going to compare the itty bitty Grade 7 to the maturing Grade 8

Here we go.

Reminder: Is not positive 5, nonononono.
Its Have 5 and Owe 6

-------------------------------------------------------------------------------------------------------------------------------------

Lets Advance on now

Look at some of these questions:

2 -5=          (-8) -5=

6 - (-9)=          (-2) - (-5)=


Let me explain how

Some word examples are:
Remove- Have 6 remove owe 9 or 16
And- Have 4 and Owe 3 or Have 1

Ceci's Scribe Post

Adding and Subtracting integers  (with no brackets)

Examples:

      (combining)

       - 7 + 2 = - 5

owe 7 & have 2 = owe 5

－ － － － － － －　＝　negative 5

＋＋

              -7

      <————— 0

<————|———|————>

　　——>-5

          +2 

we owed 7 dollars, but we have 2 dollars, how much do we have now?

we owed more than we have so the answer has to be negative, 

7-2 = 5, because we owed more, so the answer is -5.

     (removing)

- Ｔo add or subtract something that's not there,

   you must add zero pairs.

    (only happens when you see two negative sign or two subtract sign right besides each other...)

 Ｅxample:

        

                (-7) - (-10) = +3 

owe 7 remove owe 10= have 3

－－－－－－－－－－－－－－－－－

　　　　　　　＋＋＋＋＋＋＋＋＋＋　＝　+３

we owed 7 dollars, but we want to re move 10 dollars from 7 dollars,

 you can't do it, so we have to add zero pairs, we have to add 10 

zero pairs, then remove 10 dollars, we have 7 zero pairs and 3 dollars

 left, we cross out the zero pairs then we get positive 3 (3 dollars).

more examples:

             (-1) - 2 = -3  we don't need to remove because the two negative signs aren't beside each other.

owe 1 & owe 2 = owe 3

             5 - (-2) = +7

have 5 remove owe two = have 7

            -7 + 8= +1

  owe 7 & have 8= have 1

           

            2 + (-5) = -3

  have 2 & owe 5 = owe 3

Pam's Scribe Post

 today's lesson:

January 8, 2014
 (all answers at the end of explanation)
 

       Integers not only have adding in them, but subtracting, or removing. A rule you must know is "Whenever something is not there, you must add a zero pair"
A stragety you can use when you want to recongnize when to say "and" (add or combine) or "remove" is when the equation is a double negative or it's a negative and a negative, if not, then always combine unless you remove a negative (negative and negative). When you have a negative and a negative, you must add a zero pair since that negative isn't there.

negative minus negative (with brackets)

 



For example, (-5) - (-6) =
For the words, it would be :
Owe 5 Remove Owe 6.

Since you are trying to remove (-6), you can't since there isn't so you do a zero pair.

++++++
- - - - - -     <--- This evens them out and then you remove the (-6) so you are left with positive 6.

Here  you would remove the (-6) since it's part of the equation.
Then you combine (-5) since integers is all about combining.

+ + + + + +
-  -  -  -  -

You have one positive left over, therefore, the answer is (+1) or have 1.

 

positive minus negative (no brackets)

 

And example for a positive minus negative equation is:

9 - 1 =

This may seem like a regular subtracting question, but it really is like saying (+ 9) - (-1).

The minus sign actually is part of the one since it means that the one is negative.

A way this might be easier is to say the equation out loud or put it in words like so:

             have 9, owe 1.

To show this you would have 9 positives (have is positive), and 1 negative (owe is negative).

 

+ + + + + + + + +

 -



The zero pair cancels one of the positives and one of the negatives, leaving behind only 8 positives. The answer would be (+8) or have 8.

negative minus negative ( first one has no brackets)

 

This may seem different from the first one, but it's all about how you look at it.

An example of this type is : -4 - (-6) =

The only difference for this is that the negative 4 doesn't have brackets.

In words this would be : Owe 4 REMOVE Owe 6.

In pictures or in integer chips this would be 6 zero pairs, removing the minus, and you add the positives with the negative which is negative 4.

 

-  -  -  -  -  -

+ + + + + +

 

Then COMBINE the positive 6 with the negative 4.

 

+ + + + + +

-  -  -  - 

 

Then you have 2 positives left over which gives you your answer of (+2). 

 

It goes with positive minus negative, example: 4-(-6)
 

positive minus negative (with brackets)

 

 

An example of positive minus negative would be:

7-(-6) =

In words this would be have 7 REMOVE owe 6. This a double negative, since there are two negatives together.

+ + + + + +
-  -  -  -  -  -

Then you combine the 6 positives together with the 7 positives, which equals 13.

 

Calculate with the zero pairs and you're done. You have one positive left over, and you answer is (+1) or have 1.

if that didn't work, here's a video. 



 

 







here's some more fun with subtracting integers (game)

 

 

Integers Subtracting Game

(if that didn't work try copying this link)

http://www.sheppardsoftware.com/mathgames/integers/FS_Integer_subtraction.htm

 

 

 

Good luck on your learning!

Joanna's Scribe Post

Subtracting Integers

2 0 1 4

♫ Whenever something is not there,

You must add a zero pair! ♫

             Whenever you're subtracting integers, you may see these types of equations...

6 - (-9) =            (-2) - (-5) =            6 - 7 =          -4 - 6 = 

Everything is combined but subtracting. You must remove when it's an equation with 2 negatives. 

6 - (-9) =        or       (-2) - (-5) = 

Instead of saying, have six and owe 9, you say, have 6 REMOVE owe 9. The positive always stays behind. If you find 2 negatives together, you always have more than what you're owing. For this question, instead of combining have 6 and owe 9, we remove the negatives. By doing so, we add zero pairs. Like this...

6- (-9) = 15

Have 6 remove owe 9 = have 15

            Step 1                 Step 2               Step 3                     Step 4    

              (-9)                Remove         +++++++++         +++++++++ ++++++    =     15

      +++++++++              -9            Add it with your             

      - - - - - - - - -       - - - - - - - - -   positive number

For this next equation, we do the same thing but instead of starting with a positive and a negative number, they will both be negative.

(-2) - (-5) = 3

Owe 2 remove owe 5 = have 3

            Step 1                 Step 2               Step 3                         Step 4    

              (-5)                 Remove            +++++                      ++ +++   = 3 

            +++++                  -5        Combine it with your         - - 

            - - - - -               - - - - -       negative number

These next equations will be different from removing. The next equations will not have 2 negatives together meaning that you'll combine without removing. 

6 - 7 =         or        -4 - 6 = 

6 - 7 = -1

Have 6 and owe 7 = owe 1

              Step 1                                          Step 2           

           ++++++          = -1                 Remove all zero 

           - - - - - -    -                      pairs and take what is left.

-4 - 6 = -10

Owe 4 and owe 6 = owe 10

For this equation, we're doing the same thing but replacing the positive number with a negative number.

               Step 1                                                            Step 2         

      - - - - - - - - - -  = -10                     For this step, you're practically combining

                                             whatever negative numbers you have with the negative sign.

Here is a video that may help you to use different equations through subtraction...

In case you need any practice for subtracting equations, please enjoy this game...

http://www.sheppardsoftware.com/mathgames/integers/FS_Integer_subtraction.htm

Hope you find subtracting easier know that you've read this.

GOOD LUCK!

January 8, 2014

Robson's Integers Scribe

This is what we learned in class.

Chips

++++++++

--

If a positive is lined up with a negative it creates a zero pair canceling those 2 out.

In this equation there are 2 negatives and 2 positives. (+8) + (-2) this will leave you with +6.

We learned that you cant do this you have to use "Have" for positive and "Owe" for negative.

So right now you "Have" 6. This equation is for little kids, we need to use a grown up equation a grade 8 one. To do this you have to do 8 + (-2) you don't need a positive sign after every positive number because it is not necessary.

 Number Line

In class we learned about number lines. <-------------0--------------> This is a number line.

So for example we use this equation and we use the number line method to solve it. ( 8 + (-2) )

This is what you need to do for a number line                     

                                                                                8--------> 

                                                                                             <-- 2 

                                                                              0--------6-----------> 

This equation leaves you with 6

This is how you do a number line.

Estimating and Calculating Integers

(69)x(-11) = -700 EST

(69)x(-11) = -759 CALCULATED

How i got this number is a mystery. I got the estimated number by breaking down the number by turning the 69 into a 70 and the 11 into a 10 its really simple. Now to imply the sign rule, since the there are different signs Positive x Negative the product will automatically turn into a negative product.