Order of Operations and Evaluating Expressions Section 1-2 Part 2

Goals Goal To use the order of operations to evaluate expressions. Rubric Level 1 – Know the goals. Level 2 – Fully understand the goals. Level 3 – Use the goals to solve simple problems. Level 4 – Use the goals to solve more advanced problems. Level 5 – Adapts and applies the goals to different and more complex problems.

Vocabulary Evaluate

Evaluating Expressions In Part 1 of this lesson, we simplified numerical expressions with exponents and learned the order of operations. Now, we will evaluate algebraic expressions for given values of the variable.

Definition Evaluate – To evaluate an expression is to find its value. To evaluate an algebraic expression, substitute numbers for the variables in the expression and then simplify the expression.

Example: Evaluating Algebraic Expressions Evaluate each expression for a = 4, b =7, and c = 2. A. b – c b – c = 7 – 2 = 5 B. ac ac = 4 ·2 = 8 Substitute 7 for b and 2 for c. Simplify. Substitute 4 for a and 2 for c. Simplify.

Your Turn: Evaluate each expression for m = 3, n = 2, and p = 9. a. mn b. p – n c. p ÷ m Substitute 3 for m and 2 for n. mn = 3 · 2 Simplify. = 6 Substitute 9 for p and 2 for n. p – n = 9 – 2 Simplify. = 7 Substitute 9 for p and 3 for m. p ÷ m = 9 ÷ 3 Simplify.

Example: Evaluating Algebraic Expressions Evaluate the expression for the given value of x. 10 – x · 6 for x = 3 First substitute 3 for x. 10 – x · 6 10 – 3 · 6 Multiply. 10 – 18 Subtract. –8

Example: Evaluating Algebraic Expressions Evaluate the expression for the given value of x. 4 2 (x + 3) for x = –2 First substitute –2 for x.4 2 (x + 3) 4 2 (–2 + 3) Perform the operation inside the parentheses. 42(1)42(1) Evaluate powers.16(1) Multiply.16

Your Turn: Evaluate the expression for the given value of x x 2 ÷ 4 for x = x 2 ÷ 4 First substitute 2 for x ÷ 4 Square ÷ 4 Divide Add.15

Your Turn: Evaluate the expression for the given value of x. (x · 2 2 ) ÷ (2 + 6) for x = 6 (x · 2 2 ) ÷ (2 + 6) First substitute 6 for x. (6 · 2 2 ) ÷ (2 + 6) Square two. (6 · 4) ÷ (2 + 6) Perform the operations inside the parentheses. (24) ÷ (8) Divide. 3

Your Turn: What is the value of -10 – 4x if x = -13?

Your Turn: What is the value of 5k 3 if k = -4?

Your Turn: What is the value of if n = -8, m = 4, and t = 2 ?

Example: Application A shop offers gift-wrapping services at three price levels. The amount of money collected for wrapping gifts on a given day can be found by using the expression 2B + 4S + 7D. On Friday the shop wrapped 10 Basic packages B, 6 Super packages S, and 5 Deluxe packages D. Use the expression to find the amount of money collected for gift wrapping on Friday.

Example - Solution: 2B + 4S + 7D First substitute the value for each variable. 2(10) + 4(6) + 7(5) Multiply Add from left to right Add.79 The shop collected $79 for gift wrapping on Friday.

Your Turn: Another formula for a player's total number of bases is Hits + D + 2T + 3H. Use this expression to find Hank Aaron's total bases for 1959, when he had 223 hits, 46 doubles, 7 triples, and 39 home runs. Hits + D + 2T + 3H = total number of bases First substitute values for each variable (7) + 3(39) Multiply Add. 400 Hank Aaron ’ s total number of bases for 1959 was 400.

U SING A V ERBAL M ODEL Use three steps to write a mathematical model. W RITE A VERBAL MODEL. A SSIGN LABELS. W RITE AN ALGEBRAIC MODEL. Writing algebraic expressions that represent real-life situations is called modeling. The expression is a mathematical model.

A PROBLEM SOLVING PLAN USING MODELS Writing an Algebraic Model Ask yourself what you need to know to solve the problem. Then write a verbal model that will give you what you need to know. Assign labels to each part of your verbal problem. Use the labels to write an algebraic model based on your verbal model. V ERBAL M ODEL Ask yourself what you need to know to solve the problem. Then write a verbal model that will give you what you need to know. Assign labels to each part of your verbal problem. Use the labels to write an algebraic model based on your verbal model. A LGEBRAIC M ODEL L ABELS

Example: Application Write an expression for the number of bottles needed to make s sleeping bags. The expression 85s models the number of bottles to make s sleeping bags. Approximately eighty-five 20-ounce plastic bottles must be recycled to produce the fiberfill for a sleeping bag.

Example: Application Continued Approximately eighty-five 20-ounce plastic bottles must be recycled to produce the fiberfill for a sleeping bag. Find the number of bottles needed to make 20, 50, and 325 sleeping bags. Evaluate 85s for s = 20, 50, and 325. s85s (20) = 1700 To make 20 sleeping bags 1700 bottles are needed. 85(50) = 4250 To make 50 sleeping bags 4250 bottles are needed. 85(325) = 27,625 To make 325 sleeping bags 27,625 bottles are needed.

Your Turn: Write an expression for the number of bottles needed to make s sweaters. The expression 63s models the number of bottles to make s sweaters. To make one sweater, 63 twenty ounce plastic drink bottles must be recycled.

Your Turn: Continued To make one sweater, 63 twenty ounce plastic drink bottles must be recycled. Find the number of bottles needed to make 12, 25 and 50 sweaters. Evaluate 63s for s = 12, 25, and 50. s63s (12) = 756 To make 12 sweaters 756 bottles are needed. 63(25) = 1575 To make 25 sweaters 1575 bottles are needed. 63(50) = 3150 To make 50 sweaters 3150 bottles are needed.

Joke Time What do you call a blind deer? No eye deer. What did the fish say when it swam into a wall? Damn. What's a cat’s favorite color? Puuuuuurrrrrple!!!!

Assignment 1.2 Pt 2 Exercises Pg. 17 – 18: #6 – 48 even