1 1 Evaluating Algebraic Expressions Preview Evaluating Algebraic

1 -1 Evaluating Algebraic Expressions Preview Evaluating Algebraic Expressions Warm Up California Standards Lesson Presentation

1 -1 Evaluating Algebraic Expressions Warm Up Evaluating Algebraic Expressions Simplify. 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 California Standards AF 1. 2 Use the correct order of operations to evaluate algebraic expressions such as 3(2 x + 5)2. AF 1. 4 Use algebraic terminology (e. g. , variable, equation, term, coefficient, inequality, expression, constant) correctly.

1 -1 Evaluating Algebraic Expressions Vocabulary Evaluating Algebraic Expressions expression variable numerical expression algebraic expression evaluate

1 -1 Evaluating Algebraic Expressions An expression is a mathematical phrase that contains operations, numbers, and/or variables. Evaluating Algebraic Expressions A variable is a letter that represents a value that can change or vary. There are two types of expressions: numerical and algebraic. A numerical expression An algebraic expression does not contain variables. contains one or more variables. Numerical Expressions Algebraic Expressions 3+2 27 – 18 4(5) x+2 p–r 4 n

1 -1 Evaluating Algebraic Expressions To evaluate an algebraic expression, substitute a given number for the variable. Then use the order of operations to find the value of the resulting numerical expression.

1 -1 Evaluating Algebraic Expressions Additional Example 1 A: Evaluating Algebraic Expressions with One Variable Evaluating Algebraic Expressions Evaluate the 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 Evaluating Algebraic Expressions Evaluate the 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 Evaluating Algebraic Expressions Evaluate the expression for the given values of the variable. 6(n + 2) – 4 for n = 5, 6, 7 n 5 Substitute Parentheses Multiply Subtract 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! Example 1 Evaluating Algebraic Evaluate each expression for the. Expressions given values 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 C Evaluating Algebraic Evaluate the expression for the Expressions given values of the variable. 5(n + 3) – 2 for n = 3, 4, 5 n 3 Substitute Parentheses Multiply Subtract 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 Evaluating Algebraic Expressions 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 Evaluating Algebraic Expressions 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. Algebraic 1. 8 c + 32 to Expressions convert the Evaluating 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 at sea level.

1 -1 Evaluating Algebraic Expressions Additional Example 3 B: Physical Science Application Use the expression 1. 8 c + 32 to convert the temperature from. Algebraic degrees Celsius to degrees Evaluating Expressions Fahrenheit. 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 Convert the temperature from degrees Celsius Evaluating Algebraic Expressions 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 Evaluating Algebraic Expressions boiling point 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 Quiz Evaluate each expression for the given value(s) of Evaluating Algebraic Expressions 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. y(27 – x) for x = 19, y = 6 48 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