Ivan's Great Book Of Integers.

Chapter One:
Grade 7 integer review.

(+4) + (-2) = +2
Positive (4) Negative (2) = Positive 2
Have 4 Owe 2 = have 2
Standard Form : 4 - 2 = 2.

Making A Zero Pair:
An example of a zero pair is (+1) + (-1).
A negative and a positive can make a zero pair because it is oppisite from each other.

Chapter Two Multiplying Integers:
Sign Rule:
Even: When you have an even amount of negative factors, the product is positive.
Odd: When you have an odd amount of negative factors, the product is negative.

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

(+2)x(+3)=+6
2 Groups Of (+3)=+6
+++
+++

(-2)x(+3)=-6
Remove Two Groups Of (+3)=-6
---
---

(-2)x(-3)=+6
Remove Two Groups Of (-3)=+6
+++
+++

Chapter Three Dividing Integers:
Sign Rule: If you have no negative or an even amount of negative signs in a division question, the quotient is positive.

2 Types Of Division:

Partitive Division:
making parts

EX.
6/2=3
6/-2=-3

Quotative Division:
Sharing your total w/ groups

EX.
(-6)/2=-3
(-6)/-2=+3

Chapter Four Order Of Operation:

Brackets
Exponents
Division
Mutiplication
Adding
Substracting

(+5)x(-3)+(-6)/(+3). First you always follow BEDMAS, so division is first in the question, after you multiply, and do the adding.

EX.
(+5)x(-3)+(-6)/(+3)=-17
(+5)x(-3)+(-2)
(-15)+(-2)
-17 is your final answer.

Nino's Great Book of Integers

Chapter 1

Grade 7 Integer Review

(+4) + (-2) = +2
Positive (4) and Negative (2) = positive 2
have 4 and owe 2 = have 2
Standard Form: 4 - 2 = -2
Making zero pairs:

-16 = +16, -5 = + 5, +6 = -6, -2 = +2,

-10 = +10, +3 = -3, +11 = -11, -9 = +9

Chapter 2 Multiplying Integers

Sign Rule:
Even: When you have an even amount of Negative factors, the product is Positive.
Odd: When you have odd amount of Negative factors, the product is Negative.

(+2)x(-3)=
2 groups of (-3)= -6
- - -
- - -
(+2)x(+3)=
2 groups of (+3)= +6
+++
+++
(-2)x(+3)=
remove 2 groups of (+3)= -6
- - -
- - -
(-2)x(-3)=
remove 2 groups of (-3)= +6
+++
+++

Chapter 3 Dividing Integers

Sign Rule:
If you have no negative or an even amount of negative signs in a division question, the quotient is positive.

There are 2 types of division:

Partitive Division:
Making parts

EX:
6/2=3

6/-2=-3

Quotative Division:
Sharing you total with groups

EX:
(-6)/2=-3

(-6)/-2=+3

Chapter 4 Order of Operations

Brackets
Exponents
Division
Multiplication
Addition
Subtraction

(+5) x (-3) + (-6) / (+3) first you always follow BEDMAS so division is first in the question

after you do the multiplication and finally you do the addition.

example.

(+5) x (-3) + (-6) / (+3) = ( -17)

(+5) x (-3) + (-2)

(-15) + (-2)

(-17)

Justin Lorenzo's Great Big Book Of Integers

Chapter 1 GRADE 7 INTEGER REVIEW

(+4)-(-4) =0
Positive 4 subtract Negative 4 = 0
You have 4 and you owe 4 = 0 or none

(+6) + (-2) = +4
Positive 6 and Negative 2 = Positive 4
You have 6 and you owe 2 = have 4

These are zero pairs:

(+4 and - 4 = 0)
0 0 0 0
0 0 0 0
= zero

(- 2 and +2 = 0)
0 0
0 0
= zero



Chapter 2 MULTIPLYING INTEGERS

SIGN RULE

Odd: When you have a odd number of negative the product is negative.
Even: When you have a even number of negative factors the product is positive.

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

0 0 0
0 0 0

(+2)x(+3)=
2 groups of (+3)=(+6)

0 0 0
0 0 0

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

0 0 0
0 0 0

0 0 0
0 0 0

(-2)x(-3)
2 groups of (-3)=6

0 0 0
0 0 0

0 0 0
0 0 0 ->
You take the negative part away


Chapter 3 DIVIDING INTEGERS

SIGN RULE

If you have no negative or an even number of negative signs in a division question, the quotient is positive.

There are 2 types of division:

Partitive division:
Partitive division is making parts.

Example:
6 divided by 2= 3

6 divided by - 2= - 3


Quotative division:
Quotative division is sharing your total, with groups.

Example:
(-6) divided by 2= -3

6 divided by (-2)= +3


Chapter 4 ORDER OF OPERATIONS WITH INTEGERS

Brackets
Exponents
Division
Multiplication
Addition
Subtraction

(+5) x (-3) + (-6) / (+3) first you always follow BEDMAS so division is first in the question

after you do the multiplication and finally you do the addition.

example.

(+5) x (-3) + (-6) / (+3) = ( -17)

(+5) x (-3) + (-2)

(-15) + (-2)

(-17)

Van's Great Big Book of Integers

CHAPTER 1
Grade 7 Integer Review

• You can use a number line to model an integer.
  
• You can also use "integer chips"to represent integers.(Integer chips are coloured disk used to represent integers;positive integers are usually red and negative integers are usually blue.).
  
  
• When subtaracting that isnt there,use a zero pair.([For example,-6 + 2=?] [use six negative chips and 2 positive chips....remove zero pairs.Then,you are left with -4.][-6 + 2 = -4])
  

Integer ala Grade 7

(+4) + (-4)= 0 (you have 4 and you owe 4,how are left? A=0)

Standard Form

(+4) + (-4) -remove the brackets(brackets are just training wheels)

= 4 - 4 -pure standard form

Removing negative part of a zero pair

Ex.10 - (-4)=? (when a term is in a bracket,remove it by using zero pairs and turn it to a positive integer)

Use 10 positive chips and 4 negative chips.Use zero pairs for the negative chips and remove the negatives.Now, you are left with 10 positive chips and another group of 4 positive chips.Add 4 and 10.(Any integer subtraction can be completed by adding the opposite integer).10 -(-4)= 10 + (+4) = 14


Star Statements

-3 -(-7)=4 (explanation:(-)integer minus another (-) integer is positive.If we use integer chips,use zero pairs for -7 and remove the negatives.Use the 3 negative chips as zero pairs for the 7positive chips.Now, you are left with 4 positive chips.)

-3-7=-10 (explanation:subtraction:adding a negative integer)

3-7=-4 (explanation:Make zero pairs.You are left with 4 negative chips)

3+7=10 (explanation:Just add them because they have the same sign[add their chips])

-3+7=4 (explanation:Make zero pairs.You are left with 4 positive chips)

CHAPTER 2

Multiplying Integers

SIGN RULES (NEGATIVE SIGNS)

Even=when you have even number of negative factors,the product is positive

Odd=when you have an odd number of negative factors,the product is negative

http://www.youtube.com/watch?v=UHIZUE5iW-c

STANDARD FORM

(2) x (-4) -remove the multiplication sign

(2)(-4) or 2(-4) -standard form of a multiplication statement

Examples of multiplication statements

a.(+4) x (+2)=8 (multiply [(+) x (+) = (+)])

b.(+5) x (-2) =-10 (multiply[(+) x (-) = (-)])

c.(-4) x (+2)=-8 (multiply[(-) x (+) =(-)])

d.(-6)x (-1) = 6 (multiply [(-) x (-) =(+)])

Another set of examples

(+2) x (+3) = 6 (Make 2 groups of 3 positive chips)

(+2) x (-3) =-6 (Make 2 groups of 3 negative chips)

(-2) x (+3)= -6 (You can change the position of terms to (+3) x (-2) or use zero pairs)

(-2) x (-3)= 6 (make two groups of -3 and apply sign rules)

Chapter 3

Dividing Integers

Two types of division

Partative Division- making parts

Ex. 6 /2=3 (make two parts of six)
(+)(+)(+)(+)(+)(+)
[(+)(+)(+) ] [(+)(+)(+)]

Quotative Division-sharing your total with groups

(-6) / 2 =-3

share 6 with 2 groups

(-1,-1,-1)=-3 (-1,-1,-1)=-3

Check by using Multiplicative Inverse

(multiply the quotient by the divisor)

(-3)(2)=-6

(2)(-3)=-6

SIGN RULES

When you have an odd number of (-) signs in a division question,the quotient is always negative.

(-6) / 2 = -3 Check:(-3)(2)=6 -multiplicative inverse and use multiplication sign rules

6 / (-2) =-3 Check:(-3)(-2)= 6

When you have an even number of (-) or (+) signs in a division question,the quotient is always positive

6 / 2 = 3 Check:(3)(2)=6

-6 /-2 =3 Check:(3)(-2)=-6

http://www.youtube.com/watch?v=_Btpi6mfXws

CHAPTER 4

ORDER OF OPERATIONS WITH INTEGERS

Order of Operations

B- BRACKETS
E-EXPONENT
D-DIVISION
M-MULTIPLICATION
A-ADDITION
S-SUBTRACTION

-Solve terms in brackets first

-Multiply and Divide from left to right

-Add and subtract from left to right

EX.

(+5) x(-3) + (-6) / (+3)

- [15] + [-6 / 3]

-(15) + (-2)

- (-17)

Thessa's Great Book of Integers

Integers - Grade 7 Review

(Adding and Subracting Integers)

(+4)+(-2)=
positive 4 AND negative 2 = positive 2
OR
you have 4 AND you owe 2 = have 2


Standard form: 4-2= 2
Make zero pairs -16 -5 +11 -2 +6 -10 -9 +3 +16 +5 -11 +2 -6 +10 +9 -3
Homework:
-3-(-7)= +4
-3-7= -10
3-7= -4
3+7= +10
-3+7= +4

Multiplying Integers 03092011.
*When brackets are touching, they multiply*

(+2)x(+3)=

OR

2 groups of (+3)= +6



(2)x(-3)= -6
OR
2 groups of (-3)



(-2)x(+3)=
OR
(+3)x(-2)= -6
Remove 2 groups of (+3)



(-2)x(-3)= +6
Remove 2 groups of (-3)



Sign Rules (negative signs)
EVEN: When you have an even number of negative factors, the product is POSITIVE.
ODD: When you have an odd number of negative factors, the produce is NEGATIVE.

Division. 03152011.

There are 2 types of division.

PARTATIVE DIVISION or Making Parts.
QUOTATIVE DIVISION or Sharing your Total with Groups.

*If you have no negative or an even number of negative signs in the division question, the quotient is positive.
(-6)/(-3)= 2


*When you have an odd number of (-) signs in a division question, the quotient is negative.
6/(-3= -2

Daddy Brackets/Square Brackets. 03172011.

a) [(-15)/(-3)] - [(+4)x(-2)]=

5 -(-8)= 13.

Two negatives make a positive.

b) (-6)-(-9) + [(-14)/(+2)]=

(-6) + (-9) + (-7)=

*Re-arrange..
(-6)+(-7)+9
-13+9= -4

c) -8+(-2) x [(4+(-1)]

-8 + (-2) x 3

-8+-6 = -14

Order of Operations 03222011.

(+5) x (-3) + (-6) ÷ (+3)=

To figure out this question I would..
use BEDMAS to tell where the Square Brackets go.
B: Brackets
E: Exponents
D: Division
M: Muliply
A: Addition
S: Subtraction

So, using this I would..

(+5) x (-3) + [(-6) ÷ (+3)]=
You find out the answer that is in the brackets.
[(-6) ÷ (+3)]= -2

Then just add on the rest of the question..
(+5) x (-3)= -15

SOOOO.....
-15 + (-2)= -17

Trish's Great Big Book Of Integers

Chapter 1 Grade 7 Integer Review

For numbers 1, 3 and 5, I used Zero pairs because I have to find something that isn't there, while for numbers 2 and 4m I just added them up because they have the same sign.

*This is for the 5th question, I forgot to take a picture of it so when I was done with the collage one this was not included to it *

Links ? Videos ? I gotcha ;)

http://www.onlinemathlearning.com/adding-integers-2.html

http://www.lessonplanet.com/search?keywords=zero+pairs+and+integers&media=lesson

Chapter 2 Multiplying Integers

1 ) Standard Form : 2 (3) =63

OR 2 groups of (+3) = +6

+++ +++ = +6

2) Remove 2 groups of -3

--- --- = -6

3) Remove 2 groups of ( +3) = -6

* 3 groups of -2

4) Remove 2 groups of -3

+++ +++

- - - - - - ( REMOVE )

You'll get +6

Sign Rules ( Negative Signs ):

When numbers of negative signs are EVEN the answer is going to be POSITIVE.

When numbers of negative signs are ODD the answer is going to be NEGATIVE.

Links :http://staff.argyll.epsb.ca/jreed/math9/strand1/integerProd.htm

http://www.learningwave.com/chapters/integers/mlt.html

CHAPTER 3 Dividing Integers

Partitive division or like making parts.

Quotitive division or sharing.

Multiplicative Inverse

is when you can't explain division.

-4 / 2 = -2

SIGN RULES :

ODD number of NEGATIVE SIGNS, the quotient is NEGATIVE.

EVEN number of NEGATIVE SIGNS , the quotient is POSITIVE.

* You like my pajamas ? ;) *

LINKS : http://www.learningwave.com/chapters/integers/div.html

http://www.mathgoodies.com/lessons/vol5/division.html

VIDEO :

Order of Operations With Integers

(+5) x (-3) + (-6) ÷ (+3) = -17

To get the answer :

You multiply first, then divide then add, and continue from left to right.

^ What Harbeck said.

So you first start with the multiplication, which is " (+5) x (-3) " for this question, and then, you'll get -15, you then go next to the division part, which is " ( -6) ÷ ( + 3) " and the answer is +2.

You then add -15 and +2 in which will equals to - 17.

Links that can help you :

http://www.nwlincs.org/mtlincs/pilotproject/math/integer&order.htm

http://www.mathgoodies.com/lessons/vol7/operations_integers.html

Want a Video ? Here you go :)

AND I`M DONE !

Tonie's Great Big Book of Integers

Chapter 1 Grade 7 Integer Review
(+4) + (-2)=

(+4) <>

Making Zero Pairs

-16 -5 +11 -2
+16 +5 -11 +2

+6 -10 -9 +3
-6 +10 +9 -3

-6 +2= -4
-6 -2= -8
-6 +10= +4
6-(-4)= 10
-2(-3)= 1
-3 - 6= -9
-3 - 2= -5

HW.
-3 (-7) = +4
-3 -7 = -10
3 -7 = 4
3 +7 = 10
-3 +7 = 4

Chapter 2: Multiplying Integers

(+2) x (+3) = +6
(2) x (3) = 6
(2) (3) = 6
If brackets are touching, they multiply
or
If a number is touching a bracket,it also multiply

(2) x (3) = 6
or
2 groups of (3) = 6
of means multiplying


(2) x (-3) = -6
or
2 groups of (-3) = -6


(-2) x (+3)
Remove 2 groups of (+3) (use zero pairs)


(-2) x (-3) = +6
^ remove 2 groups of (-3) = +6


Chapter 3: Dividing Integers

Partative Division - making parts




Quotative Division - sharing your total with groups



Chapter4: Order of Operation with Integers
To solve (+5) x (-3) + (-6) / (+3), I would first follow the BEDMAS. I'd put square brackets around (-6) / (+3). After, I would solve (+5) x (-3) and then I would add the two answers together and which would equal to -17.

(+5) x (-3) +[(-6) / (+3)] = ( -17)

(+5) x (-3) + (-2)

(-15) + (-2)

(-17)

Windy's Great Big Book of Integers

Chapter 1 Grade 7 Integer Review

(+4) + (-2) = +2

Positive (4) and Negative (2) = positive 2

have 4 and owe 2 = have 2

Standard Form:

4 - 2 = -2

Make zero pairs:

-16 = +16, -5 = + 5, +6 = -6, -2 = +2, -10 = +10,+3 = -3,+1

1 = -11, -9 = +9

Chapter 2

Multiplying Integers

(-2) x (+3)

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

remove 2 groups of (+3) --> use zero pairs remove and...

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

2 groups of (+3) = +6

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

remove 2 groups of (-3) = +6

(2) x (+3) = -6

2 groups of (-3) = -6

Sign Rule (negative signs)

Even - When you have an even number of NEGATIVE factors the product is POSITIVE.
ODD - When you have an odd number of NEGATIVE factors the product

is NEGATIVE.

Chapter 3 Division Integers

Partitive Division:

Quotative Division:

Sign Rule for Division:

Chapter 4: Order of Operations with Integers

How I would solve this problem is first follow BEDMAS I would first put brackets on (-6) ÷ (-3) so it would look like this [(6) ÷ (-3)] and you would get an answer of -2 then I solved (+5) x (-3) = -15 So then I added -15 + -2 = -17

Bennette's Great Book of Integers

CHAPTER ONE:

GRADE 7 INTEGER REVIEW.

(+4) + (-2) = -2

| ----|-- |

| --and --|____negative 2

| ---------|_____owe 2

|

|___positive 4

|___have 4

STANDARD FORM:

4-2= -2

Make zero pairs:

a) -16 = +16

b) +6 = -6

c) -5 = +5

d) -10 = +10

e) +11 = -11

f) -9 = +9

g) -2 = +2

h) +3 = -3

-6 +2 = -4

-6 -2 = -8

-6 +10 = +4

a) 6- (-4) = +10

b) -3-6 = -9

c) -2-(-3) = +1

SUBTRACTION= adding a negative integer

HOMEWORK:

-6-(-4) = -2

-10+6 = -4

6-7+2 = +11

14-(-3) = +17

* -3-(-7) = +4

* -3-7 = -10

* 3-7 = -4

* 3+7 = +10

* -3+7 = +4

CHAPTER TWO:

MULTIPLYING INTEGERS.

(+2) x (+3) or 2 groups of (+3) = 6

OF normally means multiplying in word problems.

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

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

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

(-3) x (-4) = +12

DO page. 289 Show You Know

and page 290-290 odd numbers only

HOMEWORK BOOK page 90-91

NUMBER LINE:

(+2) x (+3) = 6

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

Seatwork:

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

1(-2) x (+3) = -6 1(+3) x (-2) = -6

2(-1) x (-6) = +6 2(-4) x ( -5) = +20

(-1) x (-6) x (-1) x (-1)

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

SIGN RULE (negative signs):

EVEN- when you have an even number of negative factors, the product is positive.

ODD- when you have an odd number of negative factors, the product is negative.

HOMEWORK:

DO page 297 - textbook

page 92-93 - homework book

VIDEOS:

LINKS:

http://staff.argyll.epsb.ca/jreed/math9/strand1/integerProd.htm

http://www.mathgoodies.com/lessons/vol5/multiplication.html

http://www.basic-mathematics.com/multiplying-integers.html

CHAPTER 3:

DIVIDING INTEGERS:

Two Types of Division

6/3 = 2

How many groups of (+3) are in +6?

PARTATIVE DIVISION or Making Parts

6/3 = 2

Share 6 with 3 groups

QUOTATIVE DIVISION or Sharing Your Total with Groups

(-6) / (-3) = 2

How many groups of (-3) are in -6

Only partative will work.

6 / 3 = 2

2 x 3 = 6

3 x 2 = 6

(-6) / (-3) = 2

2 x (-3) = -6

(-3) x (2) = -6

If you have no negative or an even number of negative signs in a division question, the quotient is positive.

-6 / 3 = - 2

Share (-6) with 3 groups

QUOTATIVE DIVISION

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

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

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

6 / (-3) = -2

When you have an odd number of ( - ) signs in a division question, the quotient is negative.

You'll see something like:

ORDER OF OPERATIONS WITH INTEGERS

When solving integer problems, you need to know or decide what operation to perform.

The order of operations for integers is the same as for whole numbers and decimals.

You should always solve an integer expression or equation by:

1. Brackets. (IF there's a square bracket, do that first then the round bracket)

2. Multiply and divide in order, from left to right.

3. Add and subtract in order, from left to right.

To solve the equation :

(+5) x (-3) + (-6) ÷ (+3),

You have to follow the rules I listed up top. But as you see, the brackets used in that expression was only used as a guide, so you don't have to do something about that. So first, multiply (+5) to (-3) and you'll get (-15). Now, divide (-6) and (+3) and you'll get (-2). Lastly, add (-15) and (-2) and you'll get (-17) as your final answer.

Still having a hard time solving this? Check out this links to help you with the Order of Operations.

http://www.mathgoodies.com/lessons/vol5/intro_integers.html

http://www.mathguide.com/lessons/Integers.html

http://www.homeschoolmath.net/teaching/integers.php

VIDEOS:

Please correct me if I made any mistakes or tips on how I could make my blog better :)