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