and Algebraic Expressions 1 7 Variables and Algebraic

and Algebraic Expressions 1 -7 Variables and Algebraic Expressions Warm Up Objective Lesson Presentation Course 22

1 -7 Variables and Algebraic Expressions Warm Up Evaluate. Remember: P. E. M. D. A. S. 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) Course 2 83

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

1 -7 Variables and Algebraic Expressions Vocabulary Variable Constant Algebraic expression Evaluate Substitute 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. **Try this with your own birth year and age. 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. Course 2

1 -7 Variables and Algebraic Expressions Age 16 18 21 36 a Year born + age = year at age 1954 + 16 1954 + 18 1954 + 21 1954 + 36 1954 + a 1970 1972 1975 1990 To evaluate an algebraic expression, substitute a number for the variable. Course 2

1 -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 14 B. k = 2 Add. k+9 2+9 11 Course 2 Substitute 5 for k. Substitute 2 for k. Add.

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. Course 2

1 -7 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. 4 x – 3 for x = 2 4(2) – 3 8– 3 5 Course 2 Substitute 2 for x. Multiply. Subtract.

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 C. 18 Add. 5 x 2 + 3 x, for x = 2 5(2)2 + 3(2) Substitute 2 for x. 5(4) + 3(2) Evaluate the power. 20 + 6 26 Course 2 Substitute 15 for s. Divide. Multiply. Add.

1 -7 Variables and Algebraic Expressions Check It Out: Example 2 A Evaluate the expression for the given value of the variable. A. 3 x – 2 for x = 3 3(3) – 2 Course 2 Substitute 3 for x. 9– 2 Multiply. 7 Subtract.

1 -7 Variables and Algebraic Expressions Check It Out: Example 2 B. r ÷ 3 + r, for r = 12 Substitute 12 for r. 12 ÷ 3 + 12 4 + 12 C. 16 Add. 4 y 2 + 2 y, for y = 3 4(3)2 + 2(3) Substitute 3 for y. 4(9) + 2(3) Evaluate the power. 36 + 6 42 Course 2 Divide. Multiply. Add.

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

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

1 -7 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. 6 y – 5 for y = 7 37 4. 4 x 2 + 3 x for x = 6 162 5. 56 x + 3 y for x = 4 and y = 3 23 6. The expression 7 d gives the number of days in d weeks. Evaluate 7 d for d = 12. How many days are in 12 weeks? 84 Course 2