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Algebra Jeopardy Distributive Property Order Of Operations Evaluate Algebraic Expr. ExponentsDiagraming

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Category Distributive Property What does “distributive property” mean?

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Category Distributive Property When adding or subtracting to find sums or differences, you distribute or pull common factors from equivalent terms.

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Category Distributive Property explain why ac + bc = ( a + b )c

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Category Distributive Property ac + bc = ( a + b )c is equal because you are distributing the “c” to both the “a” and the “b”

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Category Distributive Property 63 and 56 pull out the greatest common factor (GCF) for these two products

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Category Distributive Property 63 and 56 to find the GCF for each product, multiply 9 X 7 (= 63) and 8 X 7 (=56) 7 is the common factor that is the largest or greatest, the GCF

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Category Distributive Property 24x + 18y find the GCF in these expressions

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Category Distributive Property 24x + 18y 6 is the GCF of both 24 and 18 (6 ∙ 4)X + (6 ∙ 3)y

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Category Distributive Property 24x + 18y Turn the above expression into a story problem answer with the GCF being the number of items per bag. “X” is apples and “y” is oranges. Mrs. Bauman is shopping at Safeway – how many bags of apples and oranges does she buy?

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Category Distributive Property 24x + 18y Mr. Bauman went to Safeway and bought apples “x” and oranges “y” in bags. Each bag had 6 apples or oranges in them. 24 ÷ 6 = 4 apples and 18 ÷ 6 = 3 oranges She bought 4 bags of apples and 3 bags of oranges.

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Category Order of Operations When someone says, “Use the Order of Operations” when solving algebraic expressions, what are you to do?

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Category Order of Operations Step 1 solve all operations inside parentheses/exponents Step 2 multiply and divide from left to right Step 3 add and subtract from left to right

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Category Order of Operations solve this expression by using the Order of Operations: 36 – ( ) ∙ 3

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Category Order of Operations Step 1 36 – ( ) ∙ 3 ( 11 ) Step 2 36 – 11 ∙ 3 33 Step 3 36 – 33 = 3

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Category Order of Operations solve this expression by using the Order of Operations: 2 ∙ a + 4 ∙ b when a = 3 b = 6

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Category Order of Operations Step 1: do parenthesis - none 2 ∙ a + 4 ∙ b Step 2: replace “a/b” values – multiply L to R 2 ∙ ∙ Step 3: add from L to R = 30

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Category Order of Operations solve this expression by using the Order of Operations: 3y ∙ y + 5 ∙ 2

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Category Order of Operations Step 1: do parenthesis – none/exponent 3y ∙ y + 5 ∙ = 4 ∙ 4 = 8 Step 2: multiply L to R 3y ∙ y + 5 ∙ 2 3y ∙ 3 = 9y 5 ∙ 2 = 10 Step 3: add from L to R 9y y + 10 = (9y + y) + (8 + 10) = 10y + 18

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Category Order of Operations Explain your Order of Operations strategy to solve: x + 2x + 3x + (7-1) 2

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Category Order of Operations x + 2x + 3x + (7-1) 2 Step 1: calculate parenthesis first subtract (7-1) = (6) 2 Step 2: multiply exponent second multiply (6) 2 = 6 ∙ 6 = 36 Step 3: add expression values from L to R re write expression and add like values x + 2x + 3x + 36 = 6x + 36

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Category Evaluate Algebraic Expression What is the definition of variable?

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Category Evaluate Algebraic Expression A variable is a letter or symbol used to represent an unknown number or quantity that is varied.

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Category Evaluate Algebraic Expression What is the definition of algebraic expression?

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Category Evaluate Algebraic Expression A algebraic expression a combination of one or more numbers and letters.

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Category Evaluate Algebraic Expression evaluate the expression 4x – 6 when x = 3

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Category Evaluate Algebraic Expression When x = 3 in the expression 4x – 6, then 4∙3 – 6 = 12 – 6 = 6

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Category Evaluate Algebraic Expression simplify the expression 2(3x) (5x)4 + 1

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Category Evaluate Algebraic Expression 2(3x) (5x)4 + 1 = 6x x + 1 = 6x + 20x = 26x + 5

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Category Evaluate Algebraic Expression define co-efficient, then identify them at each stage of solving the expression below 2(3x) (5x)4 + 1

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Category Evaluate Algebraic Expression a coefficient is the number that is combined with a variable (letter) in an expression 2(3x) (5x)4 + 1 = 6x x + 1 = 6x + 20x = 26x + 5

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Category Exponents What is the definition of exponent?

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Category Exponents An exponent is the small raised number that tells how many times the base number is used as a multiplication factor.

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Category Exponents What is the power of the expression 6 2 ? Then solve 6 2.

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Category Exponents The power of the expression 6 2 is the small raised is 6 ∙ 6 = 36

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Category Exponents Why does not 5 5 equal 25?

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Category Exponents The multiplication power of 5 in 5 5 means 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 5 ∙ 5 = 25 ∙ 5 = 125 ∙ 5 = 625 ∙ 5 = 3,125

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Category Exponents What is the answer to ?

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Category Exponents = (6 ∙ 6) + (3 ∙ 3) = = 45

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Category Exponents explain why: 6 8 does not equal 6 ∙ 8

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Category Exponents 6 8 does not equal 6 ∙ 8 because: the exponent 8 means to multiply the product of 6 times 6 eight times 6 ∙ 6 ∙ 6 ∙ 6 ∙ 6 ∙ 6 ∙ 6 ∙ 6 = 1,679,616 6 ∙ 8 = does not equal 1,679,616

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Category Diagraming What is the definition of diagram?

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Category Diagraming The definition of diagram is: a picture or drawing that represents an algebraic expression.

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Category Diagraming diagram the expression 2a a + 4

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Category Diagraming 2a a equals

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Category Diagraming diagram the expression x + y x + x + y + 1

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Category Diagraming x + y x + x + y + 1 X X Y Y X X 2 1 X X Y Y equals X X Y Y X X 2 1 X X Y Y

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Category Diagraming diagram the expression 5c + 2c = (5 + 2)c

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Category Diagraming 5c + 2c = (5 + 2)c C C C C C C C C C C C C C C + equals ( )c

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Category Diagraming There are “a” trucks. There are “b” boxes in each truck. There are “c” soccer balls in each box. How would you diagram this problem if you had 5 soccer balls per box, 4 boxes per truck, and 3 trucks hauling soccer balls?

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Category Diagraming

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