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1-1 Variables and Expressions 1-2 Order Of Operations CCSS: A.SSE.1a, A.SSE.1b, A.SSE.2 New Vocabulary Using Your Textbook, Define The Following: • Algebraic Expression • Variables • Term • Factors • Product • Power • Exponent • Base Definitions • Algebraic Expression- consists of sums and/or products of numbers and variables • Variables- symbols used to represent unspecified numbers or values • Term- a number, variable, or a product or quotient of numbers and variables • Factors- In a multiplication expression, the quantities being multiplied • Product- The result of a multiplication expression • Power- an expression of the form xn • Exponent- the number of times the base is used as a factor • Base- in the expression xn, it is the ‘x’ Example 1: Write Verbal Expressions 3x 4 5 z 16 2 16u 3 2 1 2 a 6b 7 Key Concept: Translating Verbal to Algebraic Expressions OPERATION Verbal Phrases Addition More than, sum, plus, increased by, added to Less than, subtracted from, difference, decreased by, minus Product of, multiplied by, times, of Quotient of, divided by Subtraction Multiplication Division Example 2: Write Algebraic Expressions • a number t more than 6 • 10 less than the product of 7 and f • two thirds of the volume v • one third of the area a Example 3: REAL WORLD • Mr. Martinez orders 250 key chains printed with his athletic team’s logo and 500 pencils printed with their Web address. Write an algebraic expression that represents the cost of the order. Example 3: REAL WORLD • Katie estimates that 1/8 of the people who order beverages also order pastries. Write an algebraic expression to represent this situation. Example 4: Common Core • A certain smartphone family plan costs $55 per month plus additional usage costs. If x is the number of cell phone minutes used above the plan amount and y is the number of megabytes of data used above the plan amount, interpret the following expressions a. 0.25x b. 2y c. 0.25x+2y+55 Example 5: Common Core • Consuelo and James are writing an algebraic expression for three times the sum of n squared and 3. Is either of them correct? Explain your reasoning C o n su elo 3( n 3) 2 J am es 3n 3 2 Order of Operations • • • • Parentheses Exponents Multiplication/Division Addition/Subtraction Example 6: Evaluate Expressions 3 5 2 4 4 5 7 3 Example 7: Order of Operations 16 8 2 14 2 3 42 2 5 20 7 8 7 11 2 Example 8: Expressions with Grouping Symbols 4 2 5(1 0 6 ) 6[3 2 ( 2 3) ] 2 2 5 3 15 9 5 4 (1 0 8) 2 0 1 5 [1 0 (3 2 ) ] 6 2 ( 4 5) 2 3(7 4 ) Example 9: Evaluating an Algebraic Expression E valuate 3 x (2 y z ) if x 4, y 5, z 3 2 3 E valuate a (3 b 5) c if a 2, b 6, c 4 2 E valuate 5 d (6 f g ) if d 4, f 3, g 12 Example 10: REAL WORLD • Science on a Sphere (SOS) demonstrates the effects of atmospheric storms, climate changes, and ocean temperature on the environment. The volume of a sphere is four thirds of pi multiplied by the radius r to the third power. a. Write an expression that represents the volume of a sphere b. Find the volume of the 3-foot radius sphere used for SOS Example 11: Common Core • Koto purchased food for herself and her friends. She bought 4 cheeseburgers for $2.25 each, 3 French Fries for $1.25 each, and 4 drinks for $4.00. Write and evaluate an expression to find how much the food cost. Example 12: Common Core • Kamilah sells tickets at Duke University’s athletic ticket office. If p represents a preferred season ticket, b represents a blue zone ticket, and g represents a general admission ticket, interpret and evaluate the following expressions: a. 45b Preferred $100 b. 15p+35g Blue Zone $80 c. 6p+11b+22g General $70 Example 13: Common Core • Write an expression using the whole numbers 1 to 5 using all five digits and addition and/or subtraction to create a numeric expression with a value of 3 Sample Solution 5+4-3-2-1