Ian's Dividing Integers Post

The Sign Rule makes integers easier. The Sign Rule is: If the question is a + and a + or a - and a - then the answer is postive. If they are have + and a - or - and a + then the answer is Negative.
++ = Positive
-- = Positive
+- = Negative
-+ = Negative

Question 1:
(+8) / (+4) =
There are 2 ways to answer this question.
1. "Share (+8) into (+4) equal groups."
2. "How many equal groups of (+4) are in (+8)?"

So, first way is to Share 8 into 4 equal groups.

The answer is +2

We are simply sharing 8 into 4 equal groups.





The second way, "How many equal groups of 4 are in 8?"

The answer is +2 also.
Since there is 2 groups of 4 in 8.




Question 2:
(-8) / (-4) =

First way: "Share (-8) into (-4) equal groups" You can't do the first way because we can't share -8 into -4 equal groups. So we have to do the second way.
Second way: "How many equal groups of (-4) are in (-8)?"
The answer is +2
It is a positive because of the Sign Rule. - and - make +.

Question 3:
(-8) / (+4) =
First way: "Share (-8) into (+4) equal groups"
Second way: "How many equal groups of (+4) are in (-8)?" We can't do the second way because there isn't an equal group of +4 in -8.

 The answer is -2.





Question 4:
(+8) / (-4) =
First way: "Share (+8) into (-4) equal groups"
Second way: "How many equal groups of (-4) are in (+8)?"
Both of them are wrong. So there is this thing called "Multiplicative Inverse"
Which is:
(-2) x (-4) = +8


Here is a video about Dividing Integers

Nicklaus' Integers Post

(If you see any mistakes, please comment)

I will label the 3 columns A,B,C. A is the left column, B is the middle column and C is the right column. I also label the rows 1-11.  I will just put the column letter and the the row number in my questions.

Question (A,4)
(-5) + (-3) = (-8)    
(because I am in Mr. Harbeck's class, I need to put the "have" and "owe" on every question. So here I go)

Owe 5 and owe 3 = owe 8

( I also have to put it into integers chips [ i don't know what you call those chips] and or to a number ling)

 Nice there are no Zero pairs, I just added all of the negative chips

 Question (A,8)
9+(-6)=3
Have 9 and owe 6 = have 3

Since there are zero pairs, i simply circled all of the zero pairs and count how many positive or negative chips there is left which in this case, there are 3 positive chips left.

Question (B,6)

8-(-7)=15

have 8 remove owe 7 = have 15

 (sorry i cant do this one on paint because there is not that much space to do this on paints)

+ + + + + + + +            - - - - - - -

+++++++                      +++++++

Question (B,7)

(-6)-9=(-15)

owe 6 owe 9 =owe 15

Question (B,9)

2-(-5)=7

have 2 remove owe 5=7 ( i added because 2 negative makes a positive so - -7 =+7)

Question(C,1)

8-(-2)= 10

Have 8 remove owe 2 =10

                                     

Saansouk's multiplying integer scribe

The Sign rule

• When multiplying integers with the same value (-2) x (-2) = the product will always be positive.
• When the value of integers are different (+2) x (-2) = the product will be negative

The Same Value:
When the first number is a (-) it means that if the the second number was a (-) you would have had to make a zero pairs and then take away the negatives.

Example: (--)(--)--->

         (++)(++)

When the first number is a (+) and the second number is a (+) you are basically doing regular multiplication.

Example: (++)(++)

The Opposite Value:

When the first number is a (+) and the second number is a (-) you are multiplying regular numbers just with a negative with it.

Example: (--)(--)

When the first number is a (-) and the second number is a (+) you are going to make a zero pairs but take away the positives.

Example: (--)(--)

                      (++)(++)--->

Number Lines:

This includes all of the sign rule example all you have to do is put how many arrows the first amount uses and then add to the number line using the second number.

Examples:

                   0

<-----------+------+--->

                   -->-->(+4)

                   0

<---+------+---------->

    (-4) <--<--

That concludes this scribe and I hope it was a good one.

Dividing Integers Scribe #2

Have ----->(+8)  ÷ (+4) <---- Groups
There are two ways to solve this problem:
1) Share (8) into 4 equal groups
++ ++ ++ ++
2) How many groups of 4 are in 8?
++++ ++++

(-8)  ÷ (-4) = 
Share (-8) into (-4) equal groups
We cant do that because we cant share negative into another negative. 
How many equal groups of (-4) are in (-8)
---- ----
(-8) ÷ (+4) =
Share (-8) into 4 equal groups
-- -- -- -- 
How many groups of (-4) are in (-8)?
(+8) ÷ (-4) =
Share (+8) into (-4) equal groups
How many groups of (-4) are in (+8)?
-2 x -4 = 8
^This is called Multiplicative Inverse ^

Janette's Dividing Integers Scribe Post

(+8) / (+4) = *using a '/' because I don't have a division thing.* 

The way to solve this question is in two ways.

1. In the words:
          "Share 8 into 4 equal groups."

(I'm gonna put in a picture because I'm lazy.) 

So pretty much, this is what it would be separated into. (Answer is obviously 2.)






Now, the second way to say this question would be,
                "How many equal groups of 4 are in 8?"

So, the answer would be 2 once again.





NEXT QUESTIONABLE QUESTION THAT MADE ME CRY OK LET'S GO

(-8) / (-4)

Share (-8) into (-4) equal groups. 
 NO. DO NOT PUT THAT. You can't share negatives into a negative amount of groups. So, we use the other statement.

How many equal groups of -4 are in -8? 2.

This is positive 2, because of the sign rule where it says "an even number of negatives will always result in a positive.".

So..yeah.

(-8) / (4)

Share -8 in 4 equal groups.

The answer is -2.





For the second way,

How many groups of 4 are in -8
Lol u loser we can't do that.

Question 4 (Final question.)

(8) / (-4) =

Share 8 in -4 equal groups. 
No.

How many groups of -4 are in 8?
Nope lol

NOW THIS IS A PART WHERE WE CRY. BECAUSE WE ARE GOING INTO SOMETHING CALLED THE MULTIPLICATIVE INVERSE.

The statement which is the Multiplicative inverse, is "What times ____ gives you ____?"

And there is a new equation for this. Now, it is:

(-2) x (-4) = +8.

Aaaaaand we're done! Yayayayayayayay

Nicklaus' multiplying integers scribe

Question #5
Write each repeated addition as a multiplication.
 A)   (+1)+(+1)+(+1)+(+1)+(+1)= 5 * 1 = 5
 B) (-6)+(-6)= 2 * -6 = -12

Question #7

 Write each expression as a repeated addition.

A)  (+3)*(+8)= (+8)+(+8)+(+8)= (+24)

B)  (+5)*(-6)= (-6)+(-6)=(-6)+(-6)+(-6)= (-30)

Question # 13

Copy and Complete each multiplication statements.

A) (+4)*(+6)= (+24)   

B) (+7)*(-2)= (-14)

C) (-1)*(+5)= (-5) 

D) (-8)*(-2)=(+16)

Question # 15

An aircraft descends at 3 m/s for 12 s. Use multiplication to represent the situation.  How far does the aircraft descend?

3*12= 36     The aircraft descend 36 m.

Question # 17

An oil rig is drilling 2 m/min. How deep is the well after the first 8 min?

2*8=16    The well is 16 m deep.