Chapter 1 Expressions, Equations, and Functions Prerequisite Skills Page xxii (page before 1)

1.1 Evaluate Expressions Objective: Evaluate Algebraic Expressions and Use Exponents

Lingo Variable: Algebraic Expression:

Scenario You and a group of friends are going to go get two pizzas, which is 16 slices of pizza. If everyone eats the same amount, how many pieces does everyone get if there’s 8 people eating? 4 people? 2 people? x people? The algebraic expression to represent this:

Evaluating Expressions Plug it in, plug it in! Example: 14/x, when x = 2

Substitute 3 for n. Multiply. = 39 Subtract. = 2 Substitute 3 for n. = 3 Divide. EXAMPLE 1 Evaluate algebraic expressions Evaluate the expression when n = 3. a. 13 n = b. 9 n = c. n – 1 = Substitute 3 for n. Add. = 11 d. n + 8 = 3 – 13 –

GUIDED PRACTICE for Example 1 = 12 = 6 = 4 Evaluate the expression when y = y 2. 8 y 3. y + 4 = – y

Two Variables 1.Evaluate 2x ÷ y when x = 3 and y = 2 2. Evaluate kn when k = 9 and n = Evaluate x/y when x = 6 and y = ½ 4. Evaluate x – y when x = ¾ and y = ½

EXAMPLE 2 Evaluate an expression Movies The total cost of seeing a movie at a theater can be represented by the expression a + r where a is the cost (in dollars) of admission and r is the cost (in dollars) of refreshments. Suppose you pay $7.50 for admission and $7.25 for refreshments. Find the total cost.

Example You are ordering a skateboard and helmet from an online store. The total weight of the two items can be represented by s + h, where s represents the skateboard and h represents the helmet. Find the total weight if the helmet weighs 1.3 kg and the skateboard weighs 5.4 kg.

Math Lingo Power Base Exponent

ProductWords Power EXAMPLE 3 Read and write powers Write the power in words and as a product. seven to the first power a five to the second power, or five squared b c.c one half to the third power, or one half cubed z to the fifth power d. z 5 z z z z z

GUIDED PRACTICE for Example 4 Evaluate the expression. 9. x 3 when x = k 3 when k = 2.5 ANSWER

GUIDED PRACTICE for Example 4 Evaluate the expression. 11. d 4 when d = ANSWER

Cubes and Squares Cube- VolumeSquare- Area

EXAMPLE 5 Evaluate a power Storage cubes Each edge of the medium-sized pop-up storage cube shown is 14 inches long. The storage cube is made so that it can be folded flat when not in use. Find the volume of the storage cube. Then find the area one square side making the cube.

Evaluate 27 ÷ 3² × 2 - 3

1.2 Objective: Use Order of Operations to Evaluate Expressions

Order of Operations Parentheses Exponents Multiplication/Division LEFT TO RIGHT Addition/Subtraction LEFT TO RIGHT

GUIDED PRACTICE for Example 1 1. Evaluate the expression 20 – 4 2 ANSWER Evaluate the expression ANSWER Evaluate the expression ANSWER 3. 10

GUIDED PRACTICE for Examples 2 and 3 Evaluate the expression. 5. 4(3 + 9) = (8 – 2 2 ) = [( 9 + 3) 4 ] = 6

GUIDED PRACTICE for Examples 2 and 3 Evaluate the expression when y = 8. = 61 y 2 – 38. = 3 12 – y – 19. = 9 10y + 1 y More examples…

1.3 Write Expressions Transfer Verbal Phrases into Expressions

Group Activity Addition Subtraction Multiplication Division

Translate to an Expression The sum of 6 and a number x Five more than a number n Does order matter with addition?

Translate to an Expression The difference of a number x and 8 A number y minus 2 7 less than a number y – When you see “less than” – Does order matter with subtraction?

Translate to an Expression 3 times a number x the product of 8 and a number n Does order matter with multiplication?

the quotient of a number x and 5 7 divided by a number x Does order matter with division? Translate to an Expression

Review When does order matter? When does order not matter? What do you do when you see “less than”?

Application The length of a building is 20 feet more than its width “w”. Write an expression for the length of the building

Application 2 A piece of ribbon “l” feet long is cut from a ribbon 8 feet long. Write an expression for the length (in feet) of the remaining piece.

Application 3 You and 4 friends have dinner at a restaurant. Everyone decides to order the special. Write an expression for the total cost of the meals

Application 4 You work with 5 other people at an ice cream stand. All the workers put their tips into a jar and share the amount equally at the end of the day. Write an expression for each person’s share (in dollars) of the tips.

Examples Using More Than One Operation 1.4 less than the quantity 6 times a number n 2.3 times the sum of 7 and a number y 3.The difference of 22 and the square of a number m 4.The quotient when the quantity 10 plus a number x is divided by 2

Examples Using More Than One Operation 5. 8 times the quantity 4 plus a number n decreased by a number x 7. The quotient of the square of a number w and 5

Clickers Question 1 Which expression represents the phrase “the product of 15 and the quantity 12 more than a number x” A · x B.( )x C.15(x + 12) D.15 · 12 + x

Clickers Question 2 Which expression represents the phrase “twice the quotient of 50 and the sum of a number y and 8” A. C. B. D.

Homework 1.3a 1.3a: 4 – 20