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Algebra Jeopardy Distributive Property Order Of Operations Evaluate Algebraic Expr. Exponents Diagraming 100 100 100 100 100 200 200 200 200 200 300 300 300 300 300 400 400 400 400 400 500 500 500 500 500 Category Distributive Property What does “distributive property” mean? Category Distributive Property When adding or subtracting to find sums or differences, you distribute or pull common factors from equivalent terms. Category Distributive Property explain why ac + bc = ( a + b )c Category Distributive Property ac + bc = ( a + b )c is equal because you are distributing the “c” to both the “a” and the “b” Category Distributive Property 63 and 56 pull out the greatest common factor (GCF) for these two products 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 Category Distributive Property 24x + 18y find the GCF in these expressions Category Distributive Property 24x + 18y 6 is the GCF of both 24 and 18 (6 ∙ 4)X + (6 ∙ 3)y 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? 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. Category Order of Operations When someone says, “Use the Order of Operations” when solving algebraic expressions, what are you to do? 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 Category Order of Operations solve this expression by using the Order of Operations: 36 – ( 2 + 9 ) ∙ 3 Category Order of Operations Step 1 36 – ( 2 + 9 ) ∙ 3 ( 11 ) Step 2 36 – 11 ∙ 3 33 Step 3 36 – 33 = 3 Category Order of Operations solve this expression by using the Order of Operations: 2∙a + 4∙b when a=3 b=6 Category Order of Operations Step 1: do parenthesis - none 2∙a + 4∙b Step 2: replace “a/b” values – multiply L to R 2∙3+4∙6 6 + 24 Step 3: add from L to R 6 + 24 = 30 Category Order of Operations solve this expression by using the Order of Operations: 3y ∙ 3 + 42 + y + 5 ∙ 2 Category Order of Operations Step 1: do parenthesis – none/exponent 3y ∙ 3 + 42 + y + 5 ∙ 2 42 = 4 ∙ 4 = 8 Step 2: multiply L to R 3y ∙ 3 + 42 + y + 5 ∙ 2 3y ∙ 3 = 9y 5 ∙ 2 = 10 Step 3: add from L to R 9y + 8 + y + 10 = (9y + y) + (8 + 10) = 10y + 18 Category Order of Operations Explain your Order of Operations strategy to solve: x + 2x + 3x + (7-1)2 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 Category Evaluate Algebraic Expression What is the definition of variable? Category Evaluate Algebraic Expression A variable is a letter or symbol used to represent an unknown number or quantity that is varied. Category Evaluate Algebraic Expression What is the definition of algebraic expression? Category Evaluate Algebraic Expression A algebraic expression a combination of one or more numbers and letters. Category Evaluate Algebraic Expression evaluate the expression 4x – 6 when x = 3 Category Evaluate Algebraic Expression When x = 3 in the expression 4x – 6 , then 4∙3 – 6 = 12 – 6 = 6 Category Evaluate Algebraic Expression simplify the expression 2(3x) + 4 + (5x)4 + 1 Category Evaluate Algebraic Expression 2(3x) + 4 + (5x)4 + 1 = 6x + 4 + 20x + 1 = 6x + 20x + 4 + 1 = 26x + 5 Category Evaluate Algebraic Expression define co-efficient, then identify them at each stage of solving the expression below 2(3x) + 4 + (5x)4 + 1 Category Evaluate Algebraic Expression a coefficient is the number that is combined with a variable (letter) in an expression 2(3x) + 4 + (5x)4 + 1 = 6x + 4 + 20x + 1 = 6x + 20x + 4 + 1 = 26x + 5 Category Exponents What is the definition of exponent? Category Exponents An exponent is the small raised number that tells how many times the base number is used as a multiplication factor. Category Exponents What is the power of the expression 6 2 ? Then solve 6 2 . Category Exponents The power of the expression 6 2 is the small raised 2. 6 2 is 6 ∙ 6 = 36 Category Exponents Why does not 5 5 equal 25? 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 Category Exponents What is the answer to 6 2 + 3 2 ? Category Exponents 6 2 + 3 2 = (6 ∙ 6) + (3 ∙ 3) = 36 + 9 = 45 Category Exponents explain why: 6 8 does not equal 6 ∙ 8 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 = 48 48 does not equal 1,679,616 Category Diagraming What is the definition of diagram? Category Diagraming The definition of diagram is: a picture or drawing that represents an algebraic expression. Category Diagraming diagram the expression 2a + 3 + a + 4 Category Diagraming 2a + 3 + a + 4 3 4 equals 3 4 Category Diagraming diagram the expression x+y+2+x+x+y+1 Category Diagraming x + y+ 2 + x + x + y + 1 X Y 2 X X Y 1 equals X X X Y Y 2 1 Category Diagraming diagram the expression 5c + 2c = (5 + 2)c Category Diagraming 5c + 2c = (5 + 2)c C C C C C + C C equals ( )c 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? Category Diagraming