Chapter 1 - Foundations of Algebra Algebra I

Table of Contents 1.6 - Order of Operations 1.7 - Simplifying Expressions 1.8 - Introduction to Functions

1.6 - Order of Operations Algebra I

1-6 Algebra 1 (bell work) The first letter of these words can help you remember the order of operations. Please Excuse My Dear Aunt Sally Parentheses Exponents Multiply Divide Add Subtract Order of Operations Perform operations inside grouping symbols. First: Second: Evaluate powers. Third: Perform multiplication and division from left to right. Perform addition and subtraction from left to right. Fourth:

1-6 Example 1 Simplifying Numerical Expressions 1 2 A. 15 – 2 · 3 + 1 8 ÷ · 3 15 – 2 · 3 + 1 16 · 3 15 – 6 + 1 48 10 B. 12 – 32 + 10 ÷ 2 –20 ÷ [–2(4 + 1)] 12 – 32 + 10 ÷ 2 –20 ÷ [–2(4 + 1)] 12 – 9 + 10 ÷ 2 –20 ÷ [–2(5)] 12 – 9 + 5 –20 ÷ –10 8 2

Evaluate the expression for the given value of x. 1-6 Example 2 Evaluating Algebraic Expressions Evaluate the expression for the given value of x. 10 – x · 6 for x = 3 42(x + 3) for x = –2 10 – x · 6 42(x + 3) 10 – 3 · 6 42(–2 + 3) 10 – 18 42(1) –8 16(1) 16

14 + x2 ÷ 4 for x = 2 (x · 22) ÷ (2 + 6) for x = 6 14 + x2 ÷ 4 1-6 14 + x2 ÷ 4 for x = 2 (x · 22) ÷ (2 + 6) for x = 6 14 + x2 ÷ 4 (x · 22) ÷ (2 + 6) 14 + 22 ÷ 4 (6 · 22) ÷ (2 + 6) 14 + 4 ÷ 4 (6 · 4) ÷ (2 + 6) 14 + 1 (24) ÷ (8) 15 3

Math Joke Q: Why are the parentheses wearing blue ribbons? 1-6 Math Joke Q: Why are the parentheses wearing blue ribbons? A: Because they always come first

Simplify. –8 + 22 –8 + 22 1-6 Example 3 Simplifying Expression with Other Grouping Symbols Simplify. 2(–4) + 22 42 – 9 3|42 + 8 ÷ 2| 3|42 + 8 ÷ 2| –8 + 22 42 – 9 3|16 + 8 ÷ 2| 3|16 + 4| –8 + 22 16 – 9 3|20| 14 7 3 · 20 60 2

5 + 2(–8) (–2) – 3 |4 – 7|2 ÷ –3 |–3|2 ÷ –3 32 ÷ –3 9 ÷ –3 –3 1-6 3 (–2) – 3 |4 – 7|2 ÷ –3 3 |–3|2 ÷ –3 5 + 2(–8) –8 – 3 32 ÷ –3 9 ÷ –3 –3 5 + (–16) – 8 – 3 –11 1

A. the sum of the quotient of 12 and –3 and the square root of 25 1-6 Example 4 Translating from Words to Math Translate each word phrase into a numerical or algebraic expression. A. the sum of the quotient of 12 and –3 and the square root of 25 B. the difference of y and the product of 4 and the quotient of y and 2

1-6 Translate the word phrase into a numerical or algebraic expression: the product of 6.2 and the sum of 9.4 and 8. 6.2(9.4 + 8)

1-6 Example 5 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, 5 Deluxe packages D. Use the expression to find the amount of money collected for gift wrapping on Friday. 2B + 4S + 7D 2(10) + 4(6) + 7(5) 20 + 24 + 35 44 + 35 79 The shop collected $79 for gift wrapping on Friday.

HW pg.43 1.6 14-23, 25-35 (Odd), 50-54, 67, 85-88 Ch: 65, 66

1.7- Simplifying Expressions Algebra I

1-7 Algebra 1 (bell work) Pg. 46 Pg. 47

1-7 Example 1 Using the Commutative and Associative Properties Simplify. 45 + 16 + 55 + 4 45 + 55 + 16 + 4 (45 + 55) + (16 + 4) (100) + (20) 11(5) 120 55

1-7 Simplify. 1 2 • 7 • 8 410 + 58 + 90 + 2 410 + 90 + 58 + 2 1 2 • 8 • 7 (410 + 90) + (58 + 2) ( ) 1 2 • 8 7 (500) + (60) 4 • 7 560 28 21

1-7 Example 2 Using the Distributive Property with Mental Math 5(59) 8(33) 5(50 + 9) 8(30 + 3) 5(50) + 5(9) 8(30) + 8(3) 250 + 45 240 + 24 295 264

1-7 The terms of an expression are the parts to be added or subtracted. Like terms are terms that contain the same variables raised to the same powers. Constants are also like terms. Like terms Constant 4x – 3x + 2 A coefficient is a number multiplied by a variable. Like terms can have different coefficients. A variable written without a coefficient has a coefficient of 1. Coefficients 1x2 + 3x

Math Joke Q: Why was the math teacher upset with Cupid? 1-7 Math Joke Q: Why was the math teacher upset with Cupid? A: He kept changing “like terms” to “love terms”

1-7 Example 3 Combining Like Terms 0.5m + 2.5n 7x2 – 4x2 = (7 – 4)x2 = (3)x2 0.5m + 2.5n = 3x2 0.5m + 2.5n

1-7 Example 4 Simplifying Algebraic Expressions Just Watch Simplify 14x + 4(2 + x). Justify each step. Procedure Justification 1. 14x + 4 (2 + x) Distributive Property 2. 14x + 4(2) + 4(x) Multiply. 3. 14x + 8 + 4x Commutative Property 4. 14x + 4x + 8 5. (14x + 4x) + 8 Associative Property 6. 18x + 8 Combine like terms.

1-7 Simplify 6(x – 4) + 9. Justify each step. Procedure Justification 1. 6(x – 4) + 9 2. 6(x) – 6(4) + 9 Distributive Property Multiply. 3. 6x – 24 + 9 Combine like terms. 4. 6x – 15

HW pg. 49 1.7 21-35 (Odd), 45, 52-54, 67-75 (Odd) Ch: 57, 58

1.8 - Introduction to Functions Algebra I

Points on the coordinate plane are described using ordered pairs. 1-8 Algebra 1 (bell work) Points on the coordinate plane are described using ordered pairs. An ordered pair consists of an x-coordinate and a y-coordinate and is written (x, y). Points are often named by a capital letter.

Graph each point. A. T(–4, 4) B. U(0, –5) C. V (–2, –3) 1-8 Example 1 Graphing Points in the Coordinate Plane Graph each point. A. T(–4, 4) B. U(0, –5) C. V (–2, –3) Go over using graph paper, Vs accurate graphs on notebook

A. E Quadrant ll B. F no quadrant (y-axis) C. G Quadrant l D. H 1-8 Example 2 Locating Points in the Coordinate Plane •E •F •H •G y A. E Quadrant ll B. F no quadrant (y-axis) C. G Quadrant l D. H Quadrant lll

1-8 When you substitute a value for x, you generate a value for y. The value substituted for x is called the input, and the value generated for y is called the output. Output Input y = 10x + 5

Write a rule for the engraver’s fee. 1-8 Example 3 Application An engraver charges a setup fee of $10 plus $2 for every word engraved. Write a rule for the engraver’s fee. Write ordered pairs for the engraver’s fee when there are 5, 10, 15, and 20 words engraved. Let y represent the engraver’s fee and x represent the number of words engraved. Engraver’s fee is $10 plus $2 for each word y = 10 + 2 · x y = 10 + 2x

Number of Words Engraved Rule Charges Ordered Pair x (input) 1-8 Number of Words Engraved Rule Charges Ordered Pair x (input) y = 10 + 2x y (output) (x, y) 5 y = 10 + 2(5) 20 (5, 20) 10 y = 10 + 2(10) 30 (10, 30) 15 y = 10 + 2(15) 40 (15, 40) 20 y = 10 + 2(20) 50 (20, 50)

Math Joke Q: Why was the math teacher upset with one of the students? 1-8 Math Joke Q: Why was the math teacher upset with one of the students? A: He kept asking, “What’s the point?”

Input Output Ordered Pair 1-8 Example 4 Generating and Graphing Ordered Pairs Generate ordered pairs for the function using the given values for x. Graph the ordered pairs and describe the pattern. y = 2x + 1; x = –2, –1, 0, 1, 2 • Input Output Ordered Pair x y (x, y) –2 2(–2) + 1 = –3 (–2, –3) –1 2(–1) + 1 = –1 (–1, –1) 2(0) + 1 = 1 (0, 1) 1 2(1) + 1 = 3 (1, 3) 2(2) + 1 = 5 2 (2, 5) The points form a line.

Input Output Ordered Pair 1-8 y = x2 – 3; x = –2, –1, 0, 1, 2 Input Output Ordered Pair x y (x, y) –2 (–2)2 – 3 = 1 (–2, 1) –1 (–1)2 – 3 = –2 (–1, –2) (0)2 – 3 = –3 (0, –3) 1 (1)2 – 3 = –2 (1, –2) (2)2 – 3 = 1 2 (2, 1) The points form a U shape.

HW pg. 57 1.8 17-20 (Use 1 Graph), 21-27, 29, 36, 37, 67-71 (Odd) Ch: 41, 42-47