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         

                                    

NICKNAC'S SCRIBE POST

(+5)X(+5) USING A NUMBER LINE
+5           +5         
_____>_____>   +10
__________




                     
SIGN RULE

WHEN YOU HAVE THE SAME VALUE (++) YOUR PRODUCT IS GOING TO BE POSITIVE

WHEN YOU HAVE A DIFFERENT VALUE(+-) YOUR PRODUCT IS GOINIG TO BE NEGATIVE

(+10) X (+4)= 40


(+6) X (-5)= -30







ESTIMATING BIG INTEGER NUMBER


+37   +22   ESTIMATE    (+40) X (+20)= 800  

Pam's Scribe Post

integers lesson

 

When multiplying integers, here is the basic lesson.
Here's an example:
(+7) x (+2)=
In words, this would be seven groups of positive 2.
In repeated addition: (+2) + (+2) + (+2) + (+2) + (+2) + (+2) + (+2) =
You could use integer chips as so:

The red symbolizes positive.

You can also represent this equation as a number line, either vertical or horizontal.

And you'll have your answer, which is (+14).

Here's something new:

scribe rule

 

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

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

 

Let's apply this rule.

(+5) x (+4) =

Just multiply and then see whether or not the signs match or not.

5x4= 20

both positive, so the answer is positive.

(+ 5) x (+4) = +20)

 

(-6) x (+2)=

Multiply, 6x2= 12

They have different signs, meaning it's negative.

 

(-7) x (-8)=

Find the answer of 7x8, = 56

Then to see whether 56 or the answer is positive or negative, check the signs.

The two signs are the same, meaning the answer is going to be positive.

= (+56)

 

sign rule part 2

 

When multiplying integers , count the negative signs. When the number turns out to be an even number, it is going to be a positive product, and an odd number while counting equals to a negative product.

 

For example: (+4) x (+6) x (-7) x (-1) =

count the negative signs, and there are 2.

2 is an even number, therefor the answer will turn out to be a positive product.

 

To solve it, just do order of operations.

 

(+4) x (+6) x (-7) x (--1) =

(+24) x (-7) x (-1) =





(-168) x (-1)=
(+168) = answer. :)
See, it's a positive product.

Let's try this again.
(-4) x (-1) x (-3) x (+2) =
by following the same rule from before, this must be a negative product since there are 3 negative signs, and 3 is odd.

(-4) x (-1) x (-3) x (+2) =
(+4) x (-3) x (+2) =
(-12) x (+2)=
(-24) = answer
                                       
Let's try with more factors.
(-4) x (+2) x (-1) x (+1) x (-5) x (+1) =
There are 3 negatives, and 3 is an odd number meaning that the answer is going to be a negative product.

(-4) x (+2) x (-1) x (+1) x (-5) x (+1) =
(-8) x (-1) x (+1) x (-5) x (+1) =
(+8) x (+1) x (-5) x (+1) =
(+8) x (-5) x (+1) =
(-40) x (+1) =
(-40)= answer.
See it wasn't that bad.
If you're having problems with multiplying integers, please refer to the video below,




















P
Please feel free to play this game, and apply the sign rules to your answers. :)


Integer Multiplication Game

Have fun, and Good Luck! :)

Joanna's Scribe Post

Multiplying Integers

January 13, 2014

    There are 4 different kinds of equations that you'll might come across whenever you are multiplying integers.

Here are some examples...

(+2) x (+6)                (+2) x (-6)

These two equations have one important thing in common. Both equations are able to make groups or in other words, you are using repeated addition. 

What is repeated addition?

How do you make groups?

Repeated addition is another way of multiplying. Instead, we add the groups of numbers we need. In this situation, the equation is...

 (+2) x (+6)

Repeated Addition is simple...         (+6) + (+6) = (+12)

As you can see, we are technically adding instead of multiplying. 

The equation asks you for 2 groups of +6 meaning, you should end up with 2 positive 6s'

                      two groups of 6                                                              (+6) + (+6) = 12  

                                     words                                                                                            repeated addition

Here is another equation that relates to making groups

(+2) x (-6) 

This is a different equation because instead of making groups of positive numbers, you are making groups of negatives. The steps are still the same.

You have two groups of (-6)

(-6) + (-6) = (-12)

              two groups of negative six                                                    (-6) + (-6) = (-12)  

                                  words                                                                                                repeated addition

The next equations will be a little different. Instead of making groups, we are removing them.

(-3) x (+3)                        (-3) x (-3)

The trick is to add zero pairs

♫ Whenever something is not there, You must add a zero pair! ♫

(-3) x (+3) 

In words this would be, remove two groups of three

You must indicate the arrows pointing out. This will show that you are removing.

Remove two groups of positive three = owe 9

(-3) x (-3) 

Remove three groups of negative three = have 9

Making groups - join the party

Removing groups - leave the party

Here's a video that I hope will make it easier for you to understand multiplying integers

           

Also, if you feel the need for a game to help you with this topic, try this game out!

http://www.mathplayground.com/ASB_IntegerWarp.html

Thanks For Reading

&

Good Luck!