Robin's Great Book of Integers

Chapter 1
Grade 7 Review


(10)+(-7)=3
have 10 and owe 7
Bracket: These are put in for us for training us for grade 8.

Zero Pairs: This when a positive and negative are put together to make a Zero Pairs

1+(-1)=0

Used in addiction,Times, and dividing

Chapter 2
Sign Rules

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.

(2)x(2)=4
(+4)x(+4)=+16
3(5)=15
(3)(3)=6 *Standard form*


(3)x(3)
3 Groups of 3= 9

(3)x(-3)
3 groups of (-3)=-9

(-3)x(-3)
Remove 3 groups of 3

-











(-3)x(=3)
Remove 3 groups(-3)

Same as the other picture.


Chapter 3
Sign Rules

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

There are 2 types of division:

Partitive division

Partitive division is making parts.

Example:
3divided by 2= 1


Qualitative division:

Qualitative division is sharing your total, with groups.

Example:
(-3) divided by 2= -1


Chapter 4
ORDER OF OPERATIONS WITH INTEGERS

Brackets
Exponents
Division
Mmultiplication
Aaddition
Ssubtraction

First is to check if there any bracket and exponents if not skip it.
If there Division then you do first on the question.then if there multiplication then you do it second.Then Final do is addition to solve the question.

(+5) x (-3) + (-6) / (+3)
(+5) x (-3) + (-2)
(-15) + (-2)
= (-17)

rowell's Great Big Book of Integers post

Chapter 1 Grade 7 Integer Review

Include positive and negative whole number and zero

Integer chips are colored disk that represented by integer

Ex;+1 and -1

zero pair includes one + and one - .

zero pair represented zero .

Integer addition can model using integer chips or diagram.

Ex; +1 + -1 = 0

CHAPTER 2 Multiplying Integers

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.

ex; (-2) x (-5) = +10

remove 2 groups of negative 5

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 or making parts

ex; 6 /2=3 (make two parts of six)

Quotative Division or sharing your total with groups

ex; (-6) / 2 =-3 share 6 with 2 groups

Chapter 4 Order of Operations with Integers

The order of Operations is called BEDMAS :

Brackets, Exponents, Division, Multiplication, Addition, Subtraction.

ex;

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

- [5 - (-3)] + [-6 / 3]
-(8) + (-2)
- 6

Order of Operations
-Solve terms in brackets first
-Multiply and Divide from left to right
-Add and subtract from left to right

Casey's Great Big Book of Integers

Chapter 1 INTEGERS

Grade 7 Review:

- Number line

- Integer chips

- O = POSITIVE 1

- O = NEGATIVE 1

- positive and negative numbers

- zero pairs OO

Chapter 2 MULTIPLYING INTEGERS

Sign Rule:

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 DIVIDING INTEGERS

*When you have an odd number of negatives in a division question the quotient is negative*

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 muliplication

and finally you do the addition so it should look like this:

and p.s always re write the question.

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

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

(-15) + (-2)

(-17)

Daniel'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, +11 = -11, -9 = +9


CHAPTER 2 Multiplying Integers

(+2)x(+3) = +6
(2)x(3) = 6
(2)(3) = 6 *Standard form*
2(3) = 6


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

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

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

(-2)x(+3) = -6
remove 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 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 or making parts
6÷3=2 ,
how many groups of 3 are in 6?

Quotative Division or sharing your total with groups
6÷3=2 , share 6 with 3 groups

6÷2 and -6÷ (-2) will give you the answer of 3 because the questions has no, or an even amount of negative signs.
(-6)÷2 and 6÷(-2) will give you the answer of -3 because the questions have an odd amount of negative signs


Chapter 4 Order of Operations with Integers

The order of Operations is called BEDMAS : Brackets, Exponents, Division, Multiplication, Addition, Subtraction

(+5) x (-3) + (-6) ÷ (+3)
(+5) x (-3) + (-2) [solved division first]
(-15) + (-2) [solved multiplication after]
= (-17) [solved addition]

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)

Kyle's Great Big Book Of Integers

Chapter 1 Grade 7 Integer Review

(+4)-(-4)
You have 4 (+4) and you owe 4 (-4)

(+4)-(-4)=0
This is a zero pair.

Make zero pairs
-6=+6
-10=+10
-19=+19
-16=+16
-11=+11
-14=+14
-63=+63

Chapter 2

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

(-2)x(+3) (+3)x(-2)=-6 or remove 2 groups of (+3) use zero pairs

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

sign rule:

Even:when you have a even number of negative factors the product is positive.

Odd:when you have a odd number of negative the product is negative


Chapter 3



Dividing integers

There are 2 types of division.

Partitive division:

Partitive division is making parts.

6÷2=3



6÷-2=-3



Quotative division:

Quotative division is sharing your total, with groups.

(-6)÷2=-3







multiplicative inverse helps when you cant explain how to divide:
6÷(-2)


Chapter 4
Order of Operations with Integers

How to solve this question,
(+5) x (-3) + (-6) ÷ (+3)=
(+5) x (-3) + [(-6) ÷ (+3)][division]
[(+5) x (-3)] + (-2)[multiplication]
(-15)+(-2)[adding]
=-17
Brackets
Exponents
Division
Multiplication
Adding
Subtracting

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

Angel's Great Big Book of Integers

Chapter 1 Grade 7 Integer Review

(+4) + (-4) = 0
have 4 owe 4
*Brackets are training wheels. Pure standard form: 4 - 4-

Zero pair = When subtracting something that isn't there, use a zero pair.
Examples of zero pairs: +6 -6, +10 -10, +19 -19, +16 -16, +11-11,+14 -14, +63 -63

-3 -2 = 3-2 = subtraction = adding a negative integer.

5. -3 - (-7) = +4








6. -3 - 7 = -10

7. 3 - 7 = -4

8. 3 + 7 = 10







9. -3 + 7 = -4

Chapter 2 Multiplying Integers

(+2) x (+3) = 6
(2)x(3) = 6
(2)(3) < style="font-weight: bold;">

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

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

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

The negative sign on the first integer is saying to remove 2 groups of (+3)

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

Sign Rule (negative signs)
Even = When you have an even number of negatives factors the product is POSITIVE.
Odd = When you have an odd number of negative factors the product is negative.

Homework: 290-292 1-19 odds

HWB: 8.1 90-91

Chapter 3 Dividing Integers

2 types of division:

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

Paratative division or making parts.

6/3=2 Share 6 with 2 groups

Quotative division or sharing your total with groups

(-6)/(-3)=2

How many groups of (-3) are in (-6)? 2 groups

*Only partative will work.

6/3=2
2x3=6

3x2=6

(-6)/(-3)=2

2x(-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. When you have an odd number of (-) signs in a division question the quotient is negative.

HWB: 96 & 97

Chapter 4 Great Big Book of Integers

How I would solve this equation: (+5) x (-3) + (-6) / (+3)

First, I would follow the rules of BEDMAS, so I'd put square brackets around (-6) / (+3)

After, I would solve what (+5) x (-3)

Then I would add the two answers together which would equal to -17.

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

-15 + -2

= -17

Kathryn's Great Big Book of Integers

CHAPTER 1 GRADE 7 INTEGERS REVIEW

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

positive 4 AND negative 2

have 4 AND owe 2

STANDARD FORM (remove the + and () when not needed)

(+4)+(-2)=2

remove the brackets and the + sign because they aren't needed for the equation.

4-2=-2

have 4, owe 2=2

MAKE A ZERO PAIR

a) -16, +16 b) -5,+5 c)-11,+11 d)-2,+2

e) -6,+6 f) -10,+10 g) -9,+9 h) -3,+3

Homework:

5. -3-(-7) =+4
Owe 3 owe 7= +4

To solve this problem, use zero pairs

6. -3-7= -10
Owe 3 and owe 7= -10

To solve add -3 and -7 then you'll have -10

7. 3-7 = -4
Have 3, owe 7 = -4

To solve use zero pairs. Then remove -7. Lastly, check if there's any zero pairs.

8. 3+7 = 10

Have 3 and have 7= 10

To solve, add 3 and 7.

9. -3+7= +4
Owe 3 and have 7= +4

To solve, use zero pairs. Remove zero pairs.

CHAPTER 2- MULTIPLYING INTEGERS

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

(2)x(3) = 6

(2)(3) = 6

*Standard form*2(3) = 6

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

2 groups of (3)=+6

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

2 groups of (-3)=-6

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

remove 2 groups of (-3)=+6

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

remove 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- DIVIDING INTEGERS

Partitive Division- a type of division which means making parts

EX: 6÷3=2

(-6)÷-3 =2

Quotative- a type of division where you share your total with groups.

EX: -6÷(2)=

CHAPTER 4- Order of Operations With Integers

To solve (+5) x (-3) + (-6) ÷ (+3)=

*Squared brackets ALWAYS come first

*If there's no squared brackets use the order of BEDMAS.

*If there is division and multiplication at the same time, answer from left to right.

*If there is addition and subtraction at the same time, answer from left to right.

*Remember the sign rules!:)

STILL IN TROUBLE?

LINKS:)

http://www.mathleague.com/help/integers/integers.htm

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

VIDEOS