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1-6 Variables and Algebraic Expressions Warm Up Problem of the Day Lesson Presentation Lesson Quizzes Objective: Students evaluate algebraic expressions 1-6 Variables and Algebraic Expressions Warm Up Evaluate. 1. 5(7) – 1 34 2. 7(18 – 11) 49 3. 22 + 17 8 + 3 161 4. 36 + 15(40 – 35) 111 5. 33 + 7(12 – 4) 83 1-6 Variables and Algebraic Expressions Problem of the Day If charged per cut, how much will it cost to cut a log into eight pieces if cutting it into four pieces costs $12? $28 1-6 Variables and Algebraic Expressions Learn to evaluate algebraic expressions. 1-6 Variables and Algebraic Expressions Vocabulary variable constant algebraic expression evaluate 1-6 Variables and Algebraic Expressions Harrison Ford was born in 1942. You can find out what year Harrison turned 18 by adding the year he was born to his age. 1942 + 18 In algebra, letters are often used to represent numbers. You can use a letter such as a to represent Harrison Ford’s age. When he turns a years old, the year will be 1942 + a. 1-6 Variables and Algebraic Expressions The letter a has a value that can change, or vary. When a letter represents a number that can vary, it is called a variable. The year 1954 is a constant because the number cannot change. An algebraic expression consists of one or more variables. It usually contains constants and operations. For example, 1942 + a is an algebraic expression for the year Ron Howard turns a certain age. 1-6 Variables and Algebraic Expressions Age Year born + age = year at age 16 18 21 1954 + 16 1954 + 18 1954 + 21 1970 1972 1975 36 1954 + 36 1990 a 1954 + a To evaluate an algebraic expression, substitute a number for the variable. 1-6 Variables and Algebraic Expressions Additional Example 1: Evaluating Algebraic Expressions Evaluate k + 9 for each value of k. A. k = 5 k+9 5+9 14 B. k = 2 Substitute 5 for k. Add. k+9 2+9 11 Substitute 2 for k. Add. 1-6 Variables and Algebraic Expressions Check It Out: Example 1 Evaluate a + 6 for each value of a. A. a = 3 a+6 3+6 9 B. a = 5 Substitute 3 for a. Add. a+6 5+6 11 Substitute 5 for a. Add. 1-6 Variables and Algebraic Expressions Multiplication and division of variables can be written in several ways, as shown in the table. When evaluating expressions, use the order of operations. 1-6 Variables and Algebraic Expressions Additional Example 2: Evaluating Algebraic Expressions Involving Order of Operations Evaluate the expression for the given value of the variable. A. 4x – 3 for x = 2 4(2) – 3 8–3 5 Substitute 2 for x. Multiply. Subtract. 1-6 Variables and Algebraic Expressions Additional Example 2: Evaluating Algebraic Expressions Involving Order of Operations B. s ÷ 5 + s, for s = 15 15 ÷ 5 + 15 3 + 15 18 C. 5x2 + 3x, for x = 2 5(2)2 + 3(2) 5(4) + 3(2) 20 + 6 26 Substitute 15 for s. Divide. Add. Substitute 2 for x. Evaluate the power. Multiply. Add. 1-6 Variables and Algebraic Expressions Check It Out: Example 2A Evaluate the expression for the given value of the variable. A. 3x – 2 for x = 3 3(3) – 2 Substitute 3 for x. 9–2 Multiply. 7 Subtract. 1-6 Variables and Algebraic Expressions Check It Out: Example 2 B. r ÷ 3 + r, for r = 12 12 ÷ 3 + 12 4 + 12 16 C. 4y2 + 2y, for y = 3 4(3)2 + 2(3) 4(9) + 2(3) 36 + 6 42 Substitute 12 for r. Divide. Add. Substitute 3 for y. Evaluate the power. Multiply. Add. 1-6 Variables and Algebraic Expressions Additional Example 3: Evaluating Algebraic Expressions with Two Variables Evaluate 6 a + 4b, for a = 3 and b = 2. 6 a + 4b 6 + 4(2) 3 2+8 10 Substitute 3 for a and 2 for b. Divide and multiply from left to right. Add. 1-6 Variables and Algebraic Expressions Check It Out: Example 3 8 Evaluate w + 2x, for w = 4 and x = 2. 8 w + 2x 8 + 2(2) 4 Substitute 4 for w and 2 for x. 2+4 Divide and multiply from left to right. 6 Add. 1-6 Variables and Algebraic Expressions Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 1-6 Variables and Algebraic Expressions Lesson Quiz Evaluate n + 7 for each value of n. 1. n = 25 32 2. n =31 38 Evaluate each algebraic expression for the given value of the variables 3. 6y – 5 for y = 7 37 4. 4x2 + 3x for x = 6 162 5. 56 x + 3y for x = 4 and y = 3 23 6. The expression 7d gives the number of days in d weeks. Evaluate 7d for d = 12. How many days are in 12 weeks? 84