Ivorys Big book of Integers

Chapter 1: Grade 7 Integer Review:

Integers are are -negative- and +positive+ numbers. They can be represented as integer chips or on a number line. You get a zero pair when you have a negative and positive of the same number, example: -1 and +1 make 0.

Adding and subtracting integers:

-3-(-7)
you owe 3 and you pay back 7
=4

-3-7
you owe 3 and you owe 7
=-10

3-7
you have 3 and you owe 7
=-4

3+7
you have 3 and you have 7
=10

-3+7
you owe 3 and you have 7
=4

Chapter 2: Multiplying integers:

Sign rule: when you have an even number of negative integers the product will be positive, odd will be negative.
When you know that, multiply the numbers

- = negative integer chip
+ = positive integer chip

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

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


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


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

Chapter 3: Dividing Integers:

Partitive division is when you find out how many groups of a number is in another number. It can be shown on a number line:

6 divided by 2=3
__>__>__>
_|_|_|_|_|_|_|_
0 1 2 3 4 5 6

-6 divided by (-2)=3
<____ <____ < ___
_|__|__|__|__|__|__|__
-6 -5 -4 -3 -2 -1 0

Quotative division is sharing groups.

(-6) divided by 2=-3
------
/ \
--- ---

When both integers are the same you can use partitive or quotitive to get the answer.

Chapter 4: Order of operation with integers:

You can solve more complicated questions using order of operations. We use B.E.D.M.A.S. which stands for:
Brackets
Equations
Division
Multiplication
Adding
Subtracting
Square brackets are always done first. Using this order you can solve questions like this:

(+5)x(-3)+(-6) divided by (+3)=
[(+5)x(-3)]+[(-6) divided by (+3)]=
(-15)+(-2)=-17

Ryan's Great Big Book Of Integers

Chapter 1:

Grade 7 Integer Review

Integers could be express using a number line or integer chips.

In integers, when adding both positive and negativewith the same number they will cancel each other out making the answer a zero.

eg. (+5) + (-5) or (-5) + 5

The brackets for the integers are like training wheels for making equations more understandable
but mostly we need to use standard form.

eg. (+6) + (-6) In standard form 6 -6

Chapter 2:
Multiplying Integers

The Sign Rule:

When you have an even number of negative factors, the product will be POSITIVE.
eg. (-4) x (-4) = +16

When you have an odd number of positive factors, the product will be NEGATIVE.
eg. (+5) x (-4) = -20

Ways of showing how to multiply integers:

Positive x Positive = Positive: (+2) x (+3) = +6 , (2) x (3) = 6 , (2) (3) = 6
or
2(3) = 6
or
2 groups of (+3)

Negative x Positive = Negative: (-2) x (+3), remove 2 groups of (+3)

Negative x Negative = Positive: (-2) x (-3), remove 2 groups of (-3)

Chapter 3:
Dividing Integers

The way of reading the dividing integers is:
- How many groups of __ are in __?
- How many __'s go into __?

Partitive Division - The making of groups or parts.

Quotative Division - Sharing with groups.

The quotient of the two integers with the same sign der of Operations with Integers

B.E.D.M.A.S. is used to do the order of operations for integers which stands for:

Brackets
Exponents
Division
Multiplication
Addition
Subtraction

eg.
(+5) x (-3) + (-6) ÷ (+3) =

[(+5) x (-3)] + [(-6) ÷ (+3)] =

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

Kayla's Great Big Book of Integers

Chapter 1:
grade 7 Integer Review
______________________

With integers, you have zero pairs.

zero pairs are when you have the same number of positive integers that you do negative, and they cancel themselves out.

ex. (+3) + (-3) = 0

There doesn't have to be brackets, but for beginners, it becomes useful when you have a longer equation to solve. Standard form is what people usually use.

ex.
+4 -4
4-4 <---that is standard form.

SIGN RULE:
When you have an even number of negative factors, the product is always a POSITIVE.
When you have odd number of negative factors, the product is always a NEGATIVE.


Chapter 2:
Multiplying Integers
______________________

(+3) x (+8)
(+3)(+8)
3(+8)

(+3) x (+3) <--- that means ' three groups of plus three'
+++ +++ +++ <--- three groups of plus three
________________________________
MULTIPLYING IS REPEATED ADDITION!!!
ex.
(+1) + (+1) + (+1) =
3 x (+1) =
_______________________________

(+2) x (+3)
The 'x' means 'groups of.'

(-2) x (-3)
This means remove 2 groups of -3

1. (4) x (+2) = ++ ++ ++ ++
2. (5) x (-2) = -- -- -- -- --
3. (-4) x (2) = ---- ----
4. (-6) x (-1) = ++++++


Chapter 3:
Dividing Integers
____________________

Partitive Division: How many parts
ex. 15 ÷ (-3) = 5
There are 5 parts of 3 in 15.

Quotative Division: Sharing in groups
15 ÷ 3 = 5
There are 3 groups of 5 in 15.

When both integers are the same, you can use both Partitive or Quotative Division.
ex.
(+15) ÷ (+3)
or
(-15) ÷ (-3)


Chapter 4:
Order of Operations
____________________

When you use the order of operations, you use BEDMAS.

Brackets [and square brackets]
Exponents
Division
Multiplication
Addition
Subtraction

Square Brackets [ ], come first in the order of operations. If you see brackets in the equation, but there are also square brackets, do the square brackets first.

To solve this problem, you would use BEDMAS to get the answer.
ex.
(+5) x (-3) + (-6) ÷ (+3)=
(-15) + (-2)=
= -17

REMEMBER: two Negatives equal a Positive.

Arun's Great big Book of integers

Chapter 1: Grade 7 Integer review

In grade 7 I learned that their are 2 types of integers, positive and negative. You can do integer problems on a number line or adding and subtracting integer chips.

(number line)

(integer chips)

Questions:

-3-(-7)

-3- (-7) = +4

-3-7

-3 - 7 = -10

3-7

3-7 = -4

3+7

3=7 = +10

_______________________________________________________________________________

Chapter 2: Multiplying integers

1: (+2) x (+3)=

or 2 groups of three

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

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

or 2 groups of -3

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

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

_______________________________________________________________________________

Chapter 3: Dividing integers

Partitive division is where you know the total number of groups but are finding the number of objects that go into each group.

1: 6/2 = 3

2: -6÷ (-2)= (-3)

Quatative Division is where you know the number of objects but you are trying to find the groups.

Ex: (-6)÷2= (-3)

Sign rule:

6÷2= 3
The answer will be positive because the integers are the same sign.

-6÷ (-2)= 3
The answer will be positive because the integers are the same sign.
(-6)÷2= (-3)
The answer will be negative because the integers have different signs.

6÷(-2)= (-3)

The answer will be negative because the integers have different signs.

_______________________________________________________________________________

Chapter 4: Order of operations with integers

(+5) x (-3) + (-6) ÷ (+3)=

In this problem you need to use DMAS

This video on dividing integers really helped me out.

dividing integers