1. 2. Based on the diagram, what is the total number of students who did not participate in soccer or basketball? Name: Date: Period: EOC Practice:

I NTEGERS ???

Vocabulary: Integers = {…, -2, -1, 0, 1, 2, …} Whole Numbers = {0, 1, 2, …} Natural Numbers = {1, 2, 3, …} Name: Date: Period: Topic: To find sums, differences, products, and quotients of real numbers Essential Question: How do the rules of integers relate to the properties of real numbers and the definitions of operations?

A DDING & S UBTRACTING I NTEGERS

A DDITION R ULE 1) When the signs are the same, ADD and keep the sign. (-2) + (-4) = -6 2) When the signs are different, SUBTRACT and use the sign of the larger number. (-2) + 4 = (-4) = -2

E XAMPLES : U SE THE NUMBER LINE IF NECESSARY. 4 2) (-1) + (-3) = -4 3) 5 + (-7) = -2 1) (-4) + 8 =

= ? Answer Now

-6 + (-3) = ? Answer Now

W HEN SUBTRACTING, CHANGE THE SUBTRACTION TO ADDING THE OPPOSITE ( KEEP - CHANGE - CHANGE ) AND THEN FOLLOW YOUR ADDITION RULE. Example #1: (-7) (+7) Diff. Signs --> Subtract and use larger sign. 3 Example #2: (-7) Same Signs --> Add and keep the sign. -10

11b + (+2b) Same Signs --> Add and keep the sign. 13b Okay, here’s one with a variable! Example #3: 11b - (-2b)

W HICH IS EQUIVALENT TO -12 – (-3)? Answer Now

7 – (-2) = ? Answer Now

S IMPLIFY : 8 – 7 = 5 + (-3) = = = -9 – 3 = -2 + (-1) = -10 – (-12) = 17 – (-13) =

1) I F THE PROBLEM IS ADDITION, FOLLOW YOUR ADDITION RULE. 2) I F THE PROBLEM IS SUBTRACTION, CHANGE SUBTRACTION TO ADDING THE OPPOSITE ( KEEP - CHANGE - CHANGE ) AND THEN FOLLOW THE ADDITION RULE. Review

Absolute Value of a number is the distance from zero. Distance can NEVER be negative! The symbol is |a|, where a is any number. S AME RULE A PPLIES TO ABSOLUTE VALUE

Examples  7  =  10  =  -100  =   =  -3  = 3

|7| – |-2| = ? Answer Now

|-4 – (-3)| = ? Purple Answer Now

I NDEPENDENT P RACTICE   =   =  7 + (-8)  =  -82  + 3 =  16  - (-4) =  9 – (-5)  =

M ULTIPLYING & D IVIDING I NTEGERS

M ULTIPLYING AND D IVIDING I NTEGERS If:Then: (+3) x (-7) = (-21)(-21) ÷ (+3) = (-7) (-5) x (-4) = (+20)(+20) ÷ (-5) = (-4) (-3) x (+8) = (-24)(-24) ÷ (-3) = (+8) (+5) x (+6) = (+30) (+30) ÷ (+5) = (+6) Are the rules the same? Yes!

M ULTIPLYING AND D IVIDING I NTEGERS RULES: 1) When multiplying or dividing integers with the same signs, the answer will be positive. 2) When multiplying or dividing integers with different signs, the answer will be negative.

Positive times Positive = Positive ( + · + = +) Negative times Negative = Positive ( - · - = +) Positive times Negative = Negative ( + · - = -) Negative times Positive = Negative ( - · + = -) Multiplying & Dividing Rule: Just in case you didn’t get it!

P RACTICE : 3 -4 = = 8 3 = -9 2 = 30 ÷ -2 = -24 ÷ -6 = -4 ÷ 2 = 14 ÷ 7 =

1. A deep-sea diver must move up or down in the water in short steps in order to avoid getting a physical condition called the bends. Suppose a diver moves up to the surface in five steps of 11 feet. Represent her total movements as a product of integers, and find the product. W h a t d o e s T h i s m e a n ? Multiply (5 steps) (11 feet) (55 feet) 5 · 11 = 55

2. At noon the temperature is 8°C. If the temperature decreases 4°C per hour, what is the temperature at 6 pm? How long Is it from Noon to 6 pm? How much does the temperature decrease each hour? 6 hours - 4 degrees (6 hours)(- 4 degrees per hour) = - 24 degrees 8° + (- 24°) = - 16°C Add this to the original temp.