# 1 1 Evaluating Algebraic Expressions Warm Up Problem

1 -1 Evaluating Algebraic Expressions Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

1 -1 Evaluating Algebraic Expressions Warm Up Evaluate. 1. 21 – 2(3) 15 2. 4 + 3 9 31 3. 2(9) + (3) 21 4. 6(1. 4) + 12 20. 4 5. 7(2. 9) – 5 15. 3

1 -1 Evaluating Algebraic Expressions Problem of the Day Miss Smith obtained the prices below from the landscape company. She plans to buy five birch, two elm, one dogwood, and two oak trees. The landscape company will charge her $15 to plant each tree. How much will it cost? $337. 90 Trees Price Maple $22. 99 Dogwood $23. 99 Elm $16. 99 Crab apple $26. 99 Oak $19. 99 Birch $17. 99

1 -1 Evaluating Algebraic Expressions Learn to evaluate algebraic expressions.

1 -1 Evaluating Algebraic Expressions Vocabulary variable coefficient algebraic expression constant evaluate substitute

1 -1 Evaluating Algebraic Expressions A variable is a letter that represents a value that can change or vary. The coefficient is the number multiplied by the variable. Coefficient Variable

1 -1 Evaluating Algebraic Expressions An algebraic expression has one or more variables. In the algebraic expression x + 6, 6 is a constant because it does not change. To evaluate an algebraic expression, substitute a given number for the variable, and find the value of the resulting numerical expression. Evaluate- to find the value of a numerical or algebraic expression Substitute-to replace a variable with a number or another expression in an algebraic expression

1 -1 Evaluating Algebraic Expressions Additional Example 1 A: Evaluating Algebraic Expressions with One Variable Evaluate each expression for the given value of the variable. x – 5 for x = 12 12 – 5 7 Substitute 12 for x. Subtract.

1 -1 Evaluating Algebraic Expressions Remember! Order of Operations PEMDAS: 1. Parentheses 2. Exponents 3. Multiply and Divide from left to right. 4. Add and Subtract from left to right.

1 -1 Evaluating Algebraic Expressions Additional Example 1 B: Evaluating Algebraic Expressions with One Variable Evaluate each expression for the given value of the variable. 2 y + 1 for y = 4 2(4) + 1 Substitute 4 for y. 8+1 Multiply. 9 Add.

1 -1 Evaluating Algebraic Expressions Additional Example 1 C: Evaluating Algebraic Expressions with One Variable Evaluate the expression for the given values of the variable. 6(n + 2) – 4 for n = 5, 6, 7 n Substitute Parentheses Multiply Subtract 5 6(5 + 2) – 4 6(7) – 4 42 – 4 38 6 6(6 + 2) – 4 6(8) – 4 48 – 4 44 7 6(7 + 2) – 4 6(9) – 4 54 – 4 50

1 -1 Evaluating Algebraic Expressions Check It Out: Examples 1 Evaluate each expression for the given value of the variable. A. x + 5 for x = 3 3+5 8 Substitute 3 for x. Add. B. 4 c + 1 for c = 11 Substitute 11 for c. 4(11) + 1 Multiply. 44 + 1 Add. 45

1 -1 Evaluating Algebraic Expressions Check It Out: Example 1 Evaluate the expression for the given values of the variable. C. 5(n + 3) – 2 for n = 3, 4, 5 n Substitute Parentheses Multiply Subtract 3 5(3 + 3) – 2 5(6) – 2 30 – 2 28 4 5(4 + 3) – 2 5(7) – 2 35 – 2 33 5 5(5 + 3) – 2 5(8) – 2 40 – 2 38

1 -1 Evaluating Algebraic Expressions Additional Example 2: Evaluating Algebraic Expressions with Two Variables Evaluate each expression for the given values of the variables. A. 4 x + 3 y for x = 2 and y = 1 4(2) + 3(1) Substitute 2 for x and 1 for y. Multiply. 8+3 Add. 11 B. 9 r – 2 p for r = 3 and p = 5 Substitute 3 for r and 5 for p. 9(3) – 2(5) Multiply. 27 – 10 Subtract. 17

1 -1 Evaluating Algebraic Expressions Check It Out: Example 2 Evaluate each expression for the given values of the variables. A. 3 x + 2 y for x = 3 and y = 4 3(3) + 2(4) Substitute 3 for x and 4 for y. Multiply. 9+8 Add. 17 B. 8 q – 3 r for q = 2 and r = 2 Substitute 2 for q and 2 for r. 8(2) – 3(2) Multiply. 16 – 6 Subtract. 10

1 -1 Evaluating Algebraic Expressions Additional Example 3 A: Physical Science Application Use the expression 1. 8 c + 32 to convert the boiling point temperature from degrees Celsius to degrees Fahrenheit. Boiling point of water at sea level: 100°C 1. 8 c + 32 Substitute 100 for c. 1. 8(100) + 32 Multiply. 180 + 32 Add. 212 100°C = 212°F Water boils at 212°F.

1 -1 Evaluating Algebraic Expressions Additional Example 3 B: Physical Science Application Boiling point of water at an altitude of 4400 meters: 85°C 1. 8 c + 32 1. 8(85) + 32 Substitute 85 for c. 153 + 32 Multiply. 185 Add. 85°C = 185°F Water boils at 185°F at 4400 m. t

1 -1 Evaluating Algebraic Expressions Check It Out: Example 3 A Use the expression 1. 8 c + 32 to convert the temperature from degrees Celsius to degrees Fahrenheit. Europe’s highest recorded temperature (Seville, Spain): 50°C 1. 8 c + 32 1. 8(50) + 32 90 + 32 122 50°C = 122°F Substitute 50 for c. Multiply. Add. The highest recorded temperature in Europe is 122°F.

1 -1 Evaluating Algebraic Expressions Check It Out: Example 3 B Use the expression 1. 8 c + 32 to convert the temperature from degrees Celsius to degrees Fahrenheit. 10°C 1. 8 c + 32 1. 8(10) + 32 Substitute 10 for c. 18 + 32 Multiply. 50 Add. 10°C = 50°F

1 -1 Evaluating Algebraic Expressions Lesson Quizzes Standard Lesson Quiz for Student Response Systems

1 -1 Evaluating Algebraic Expressions Lesson Quiz Evaluate each expression for the given values of the variables. 1. 6 x + 9 for x = 3 27 2. x + 14 for x = 8 22 3. 4 x + 3 y for x = 2, y = 3 17 4. 1. 6 x – 2. 9 y for x = 19, y = 6 13 5. If n is the amount of money in a savings account, then the expression n + 0. 03 n can be used to find the amount in the account after it has earned interest for one year. Find the total in the account after one year if $500 is the initial amount. $515

1 -1 Evaluating Algebraic Expressions Lesson Quiz for Student Response Systems 1. Evaluate the expression for the given value of the variable. 6 x + 12 for x = 7 A. 23 B. 40 C. 54 D. 65

1 -1 Evaluating Algebraic Expressions Lesson Quiz for Student Response Systems 2. Evaluate the expression for the given value of the variable. k + 72 for k = 7 A. 79 B. 82 C. 96 D. 98

1 -1 Evaluating Algebraic Expressions Lesson Quiz for Student Response Systems 3. Evaluate the expression for the given values of the variables. 2 m + 2 n for m = 4, n = 5 A. 18 B. 20 C. 22 D. 24

1 -1 Evaluating Algebraic Expressions Lesson Quiz for Student Response Systems 4. Evaluate the expression for the given values of the variables. 3. 2 r – 4. 6 s for r = 20, s = 5 A. 30 B. 35 C. 39 D. 41

1 -1 Evaluating Algebraic Expressions Lesson Quiz for Student Response Systems 5. If n is the amount of money that Bill had borrowed from a bank, then the expression n + 0. 05 n can be used to find the total amount Bill has to return after one year with respect to the interest rate. How much money should Bill pay after one year if $700 is the amount borrowed? A. $710 B. $717 C. $735 D. $742

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