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

Scribe

Sign Rule (Part 1)

When integers have the same value (+ or -) the product is positive.

When the integers have different values (+,-) the product is negative

(+2)×(-3)=-6            (-2)×(+3)=-6

(+2)×(+3)=6             (-2)×(-3)=6

Sign Rule (Part 2)

When multiplying integers count the negative signs

Odd number= negative product

Even number= positive product

(+2)×(+3)×(-1)=

\            /

     (+6) × (-1)=(-6)

(+2)×(+3)×(-1)×(-1)=

 \           /

     (+6) × (-1)

Rafael's Multiplying and Dividing Scribe Post

First of all you'll need the  sign rule from adding all the way to subtracting.
The sign rules are:

If theres two of the same integers (+,-) it means the answer is positive
eg. (+4)+(+9)=+13

If the signs are different (+,-) the answer would be negative
eg. (-4)-(+9)=-13

The sign rule only works while using subtracting, dividing, multiplying, and adding
Examples:
(1.)(+4)+(+9)=+13 (2.)(-4)-(+9)=-13

(3.)(-4)-(-9)=+5 (4.)(+3)x(+2)=+6

(5.)(+3)x(-3)=-9 (6.)(-5)x(-5)=+25

(7.)(-8)÷(+4)=-2 (8.)(-8)÷(-4)=+2

(9.)(+8)÷(-4)=-2

Sentences for both multiplying and division are:

Multiplying sentences always go with groups of, like:

eg. 3 groups of +2 or +6

Dividing sentences always go with either Share no. into no. equal groups or how many groups of no. are in no., like:

eg. Share -8 into +4 equal groups or -2

eg. how many groups of -4 are in +8 or -2

These are the multiplying and dividing diagrams:

But Dividing has so much diagrams based in sentences, like:

And Dividing also has some division that can't use one of the two statements, like:

eg. (-8)÷(-4)=+2

How many groups of (-4) are in (-8)/ can't use "share" statements/ CAN BE DIAGRAMED

eg. (+8)÷(-4)=-2 

How many groups of (-4) are in (+8)/ can't use "share" statements/ CAN BE DIAGRAMED

And then there's something called the Multiplicative Inverse

Which means the multiplication statement can't be diagramed like this question, but can be stated.

eg. (-4)x(-2)=+8         

                                    

Allison's Scribe Post

Allison Concepcion's Scribe Post: How to divide integers

There are many ways to divide integers some ways will work some cannot. Dividing integers is a bit more complex than multiplying integers but the same sign rule applies. A positive and a positive equals a positive. A negative and a positive equals a negative, and a negative and a negative equals a positive.

What does ÷ mean? This symbols means you are sharing _?_ into _?_ equal groups in this case lets just say you are sharing (+8) into 2 equal groups. When you are dividing integers the numerator is what you have ( you have 8) and the denominator represents how many groups there are (you have 2 groups) e.g.

8- What you have
2- How many groups you have

First off, if you are dividing two positives, there are two possible ways to show your work.

(+8)÷(+2)= 4

Step 1: Have (+8) and have 2 groups.
Share (+8) into 2 equal groups.

Step 2: Now you share (+8) into two equal groups
Your answer will be 4

Now that you've figured out how to show your work in one way, here's another way of how to show your work.

You are asking yourself, how many groups of (+2) are in (+8)?

Step 1: have your (+8)











Step 2: Now, ask yourself how many groups of (+2) are in (+8)
There are 4 groups of (+2) in (+8)
Your answer is 4

If you are dividing a negative and a positive integers, try to use the same method as before.

(-8)÷(+4)= -2

Step 1: Share (-8) into 4 equal groups






Step 2: You share (-8) groups into 4 equal groups
Your answer is -2

 
Method 2: How many groups of (+4)  are in (-8)?
You cannot do this method because there are no groups of positive 4 in negative 8.



 X







 This time you are dividing a negative by a negative and also see if one of the two methods work.

Method 1: Share (-8) into (-4) groups.
It is not going to work because there is no such thing as (-4) equal groups.

X







Method 2: How many groups of (-4) are in (-8)?

Step 1: Have your (-8)

Step 2: Now ask yourself, how many groups of (-4) are in (-8)

                  ↓                                    ↓
             
         1 group               +            1 group             =              2 groups

         Your answer is 2.


Now, you are dividing a positive by a negative, same rules apply try the same two methods to see if one of the two methods work.

(+8)÷(-4)= -2

Step 1: Share (+8) into (-4) equal groups

X





You cannot do this method because there is no such thing as sharing positive 8 into negative 4 equal groups. 

Method 2: How many groups of (-4) are in (+8)?

                X



Once again you cannot do this method because there are no groups of (-4) in (+8)

Since none of these methods work there is another different method that we can use which is called Multiplicative Inverse. Multiplicative inverse is basically the opposite of dividing so instead od dividing to figure out the answer you have to multiply to get the answer.

Step 1: Ask your self (-4) multiplied by what will equal (+8)?

(-4)x (? ) =(+8)

Step 2: If you figure out what the missing number is that will be your answer.

(-4)x (? ) =(+8)
(-4)x(-2)= (+8)

-2 will be your answer.


You cannot show this method by using a model you can only show this method by using multiplicative inverse.

(Skip to 7:09 to learn how to divide integers)

NICNAC'S scirbe post

                                                             integer division
(+8) / (+2)= +4
share (+8) into (2) equal groups
++++     ++++
           2 equal groups
how many groups of +2 are in +8
++ ++ ++ ++


-8 / +4= -2
share -8 into 4 equal groups
-- -- -- --




-8 / -4 = +2
multiple intensive

Trina's scribe pots

                         

Sign rule part 1 

when the Integer have the same value +or- the product is positive 

when the Integer have different values (+) (-) the product is negative 

(+2 )X (+3) X (-1) X (-1) 

|_______| 

       +6 x (-1) 

          -6 x (-1) = +6 

Sign rule part 2 

when multiplying integer count the negative signs 

odd number - product 

even number + product 

(+3) x (-4) 

3 groups of 4 

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

(-2) x (+3) = -6 

remove 2 groups of 3 

_ _ _  _ _ _ 

+ + +  + + + 

do a zero pair 

If the first sign is negative you will do a zero pair