CHAPTER 1Grade 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)=-6http://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)
STANDARD FORM