2-7 Variables and Algebraic Expressions Warm Up Problem of the Day Course 2 Warm Up Problem of the Day Lesson Presentation

2-7 Variables and Algebraic Expressions Warm Up Evaluate. 1. 5(7) – 1 Course 2 2-7 Variables and Algebraic Expressions Warm Up Evaluate. 1. 5(7) – 1 2. 7(18 – 11) 3. 22 + 17  8 + 3 4. 36 + 15(40 – 35) 5. 33 + 7(12 – 4) 34 49 161 111 83

2-7 Variables and Algebraic Expressions Problem of the Day Course 2 2-7 Variables and Algebraic Expressions Problem of the Day How much will it cost to cut a log into eight pieces if cutting it into four pieces costs $12? $28

2-7 Learn to evaluate algebraic expressions. Course 2 2-7 Variables and Algebraic Expressions Learn to evaluate algebraic expressions.

Insert Lesson Title Here Course 2 2-7 Variables and Algebraic Expressions Insert Lesson Title Here Vocabulary variable constant algebraic expression evaluate

2-7 Variables and Algebraic Expressions Course 2 2-7 Variables and Algebraic Expressions Ron Howard was born in 1954. You can find out what year Ron turned 16 by adding the year he was born to his age. 1954 + 16 In algebra, letters are often used to represent numbers. You can use a letter such as a to represent Ron Howard’s age. When he turns a years old, the year will be 1954 + a.

2-7 Variables and Algebraic Expressions Course 2 2-7 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, 1954 + a is an algebraic expression for the year Ron Howard turns a certain age.

Year born + age = year at age Course 2 2-7 Variables and Algebraic Expressions Age Year born + age = year at age 16 1954 + 16 1970 18 1954 + 18 1972 21 1954 + 21 1975 36 1954 + 36 1990 a 1954 + a To evaluate an algebraic expression, substitute a number for the variable.

Additional Example 1: Evaluating Algebraic Expressions Course 2 2-7 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 Substitute 5 for k. 14 Add. B. k = 2 k + 9 2 + 9 Substitute 2 for k. 11 Add.

Insert Lesson Title Here Course 2 2-7 Variables and Algebraic Expressions Insert Lesson Title Here Try This: Example 1 Evaluate a + 6 for each value of a. A. a = 3 a + 6 3 + 6 Substitute 3 for a. 9 Add. B. a = 5 a + 6 5 + 6 Substitute 5 for a. 11 Add.

2-7 Variables and Algebraic Expressions Multiplication Division Course 2 2-7 Variables and Algebraic Expressions Multiplication and division of variables can be written in several ways, as shown in the table. Multiplication Division q 2 q/2 7t 7 · t 7(t) 7  t q ÷ 2 s r ab a · b s/r a(b) a  b s ÷ r When evaluating expressions, use the order of operations.

2-7 Variables and Algebraic Expressions Course 2 2-7 Variables and Algebraic Expressions Additional Example 2A: 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 Substitute 2 for x. Multiply. 8 – 3 5 Subtract.

2-7 Variables and Algebraic Expressions Course 2 2-7 Variables and Algebraic Expressions Additional Example 2B & 2C: Evaluating Algebraic Expressions Involving Order of Operations B. s ÷ 5 + s, for s = 15 15 ÷ 5 + 15 Substitute 15 for s. 3 + 15 Divide. 18 Add. C. 5x2 + 3x, for x = 2 5(2)2 + 3(2) Substitute 2 for x. 5(4) + 3(2) Evaluate the power. 20 + 6 Multiply. 26 Add.

Insert Lesson Title Here Course 2 2-7 Variables and Algebraic Expressions Insert Lesson Title Here Try This: Example 2A Evaluate each expression for the given value of the variable. A. 3x – 2 for x = 3 3(3) – 2 Substitute 3 for x. Multiply. 9 – 2 Subtract. 7

Insert Lesson Title Here Course 2 2-7 Variables and Algebraic Expressions Insert Lesson Title Here Try This: Example 2B & 2C B. r ÷ 3 + r, for r = 12 12 ÷ 3 + 12 Substitute 12 for r. 4 + 12 Divide. 16 Add. C. 4y2 + 2y, for y = 3 4(3)2 + 2(3) Substitute 3 for y. 4(9) + 2(3) Evaluate the power. 36 + 6 Multiply. 42 Add.

2-7 Variables and Algebraic Expressions Course 2 2-7 Variables and Algebraic Expressions Additional Example 3: Evaluating Algebraic Expressions with Two Variables 6 a Evaluate + 4b, for a = 3 and b = 2. 6 a + 4b 6 3 Substitute 3 for a and 2 for b. + 4(2) Divide and multiply from left to right. 2 + 8 10 Add.

Insert Lesson Title Here Course 2 2-7 Variables and Algebraic Expressions Insert Lesson Title Here Try This: Example 3 8 w Evaluate + 2x, for w = 4 and x = 2. 8 w + 2x 8 4 + 2(2) Substitute 4 for w and 2 for x. Divide and multiply from left to right. 2 + 4 6 Add.

Insert Lesson Title Here Course 2 2-7 Variables and Algebraic Expressions Insert Lesson Title Here Lesson Quiz Evaluate n + 7 for each value of n. 1. n = 25 2. n =31 Evaluate each algebraic expression for the given value of the variables 3. 6y – 5 for y = 7 4. 4x2 + 3x for x = 6 5. + 3y for x = 4 and y = 3 6. The expression 7d gives the number of days in d weeks. Evaluate 7d for d = 12. How many days are in 12 weeks? 32 38 37 162 56 x 23 84