Zero pairs
- a pair of integer chips with one chip representing +1 and one chip representing -1
eg. -6 +6, +10 -10, +19 -19, -16 +16, -11 +11, +14 -14, +63 -63.
Grade 7 form > (+4) + (-4) = 0
Standard form > 4 - 4 = 0
RED = (+) POSITIVE
BLUE = (-) NEGATIVE
*-3 - (-7) = +4
*-3 - 7 = -10
*3 - 7 = -4
*3 + 7 = +10
*-3 + 7 = +4
Chapter 2
Multiplying Integers
-multiplying is repeated addition
-to use something that isn't there use a zero pair
(+3)x(+8) = (+3)(+8) = 3(+8) = (+8)+(+8)+(+8)
When a bracket and another bracket are touching they "kiss" and multiply like bunnies. The same thing goes for when a number and a bracket are touching.
Chapter 3
Dividing Integers
What is Partitive Division?
You think to yourself ,"how many groups of the same size you can form?" Or, "how many times does the divisor fit into the dividend?"
eg. 6÷2= ? How many groups of 2 are in 6? +3
-6÷ (-2)= ? How many -2's go into -6? +3
What is Quotative Division?
Quotative Division is having to share equally with groups.
eg. (-6)÷2= -3
How can the Multiplicative Inverse help you solve 6÷(-2)?
Multiplicative Inverse is when you change around the numbers of the equation. It can help you solve 6÷(-2) by checking your answer. An example, 6÷(-2)=-3. To check your answer, switch it around, 6÷(-3)=-2.
Sign Rule
The quotient of two integers with the same even amount of (-) signs is positive.
The quotient of two integers with a different amount of (-) signs is negative when there is an odd number of (-) signs.
eg. 6÷2= +3 -positive because both integers are positive
-6÷ (-2)= +3 -positive because there's an even number of negative signs
(-6)÷2= -3 -negative because there is an odd number of negative signs
6÷(-2)=-3 -negative because there is an odd number of negative signs
Chapter 4
Order of Operations with Integers
BEDMAS [square brackets around division/multiplication]
eg. [(+5) x (-3)] + (-6) ÷ (+3)=
-15 +[(-6) ÷ (+3)]=
-15 + -2 = -17
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