1. Course 2 1-7 Variables and Algebraic Expressions 1-7 Variables and Algebraic Expressions Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Course 2 1-7 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. 3 3 + 7(12 – 4) 34 49 161 111 83

3. Course 2 1-7 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

4. Course 2 1-7 Variables and Algebraic Expressions Learn to evaluate algebraic expressions.

5. Course 2 1-7 Variables and Algebraic Expressions Vocabulary variable constant algebraic expression evaluate

6. Course 2 1-7 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.

7. Course 2 1-7 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.

8. Course 2 1-7 Variables and Algebraic Expressions To evaluate an algebraic expression, substitute a number for the variable. AgeYear born + age = year at age 161954 + 161970 181954 + 181972 211954 + 211975 361954 + 361990 a1954 + a

9. Course 2 1-7 Variables and Algebraic Expressions Evaluate k + 9 for each value of k. Additional Example 1: Evaluating Algebraic Expressions A. k = 5 k + 9 5 + 9 14 Substitute 5 for k. Add. B. k = 2 k + 9 2 + 9Substitute 2 for k. 11 Add.

10. Course 2 1-7 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 Substitute 3 for a. Add. B. a = 5 a + 6 5 + 6Substitute 5 for a. 11 Add.

11. Course 2 1-7 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.

12. Course 2 1-7 Variables and Algebraic Expressions Evaluate the expression for the given value of the variable. Additional Example 2: Evaluating Algebraic Expressions Involving Order of Operations A. 4x – 3 for x = 2 4(2) – 3 8 – 3 5 Substitute 2 for x. Multiply. Subtract.

13. Course 2 1-7 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. 5x 2 + 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.

14. Course 2 1-7 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 9 – 2 7 Substitute 3 for x. Multiply. Subtract.

15. Course 2 1-7 Variables and Algebraic Expressions Check It Out: Example 2 B. r ÷ 3 + r, for r = 12 12 ÷ 3 + 12 4 + 12 16 C. 4y 2 + 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.

16. Course 2 1-7 Variables and Algebraic Expressions Evaluate Additional Example 3: Evaluating Algebraic Expressions with Two Variables 6a6a + 4b, for a = 3 and b = 2. 6a6a + 4b 6363 + 4(2) 2 + 8 10 Substitute 3 for a and 2 for b. Divide and multiply from left to right. Add.

17. Course 2 1-7 Variables and Algebraic Expressions Check It Out: Example 3 Evaluate 8w8w + 2x, for w = 4 and x = 2. 8w8w + 2x 8484 + 2(2) 2 + 4 6 Substitute 4 for w and 2 for x. Divide and multiply from left to right. Add.

18. Course 2 1-7 Variables and Algebraic Expressions 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. 4x 2 + 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? 3832 37 162 56 x 23 84