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AF1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2 x + 5) 2 .

California Standards. AF1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2 x + 5) 2 . AF1.4 Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality , expression, constant ) correctly. Vocabulary. expression variable

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AF1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2 x + 5) 2 .

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  1. California Standards AF1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2x + 5)2. AF1.4 Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality, expression, constant) correctly.

  2. Vocabulary expression variable numerical expression algebraic expression evaluate

  3. An expression is a mathematical phrase that contains operations, numbers, and/or variables. 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 does not contain variables. An algebraic expression contains one or more variables.

  4. 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.

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

  6. 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.

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

  8. Additional Example 1C: 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 6(5 + 2) – 4 6(7) – 4 42 – 4 38 6(8) – 4 48 – 4 44 6(6 + 2) – 4 6(7 + 2) – 4 6(9) – 4 54 – 4 50

  9. Check It Out! Example 1 Evaluate each expression for the given values of the variable. A.x + 5 for x = 3 3+ 5 Substitute 3 for x. 8 Add. B.4c + 1 for c = 11 4(11) + 1 Substitute 11 for c. 44 + 1 Multiply. 45 Add.

  10. Check It Out! Example 1C Evaluate the expression for the given values of the variable. 5(n + 3) – 2 for n = 3, 4, 5 5(3 + 3) – 2 5(6) – 2 30 – 2 28 5(4 + 3) – 2 5(7) – 2 35 – 2 33 5(5 + 3) – 2 5(8) – 2 40 – 2 38

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

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

  13. Additional Example 3A: Physical Science Application Use the expression 1.8c + 32 to convert the temperature from degrees Celsius to degrees Fahrenheit. Boiling point of water at sea level: 100°C 1.8c + 32 1.8(100) + 32 Substitute 100 for c. 180 + 32 Multiply. 212 Add. 100°C = 212°F Water boils at 212°F at sea level.

  14. Additional Example 3B: Physical Science Application Use the expression 1.8c + 32 to convert the temperature from degrees Celsius to degrees Fahrenheit. Boiling point of water at an altitude of 4400 t meters: 85°C 1.8c + 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.

  15. Check It Out! Example 3A Convert the temperature from degrees Celsius to degrees Fahrenheit. Europe’s highest recorded temperature (Seville, Spain): 50°C 1.8c + 32 1.8(50) + 32 Substitute 50 for c. 90 + 32 Multiply. 122 Add. 50°C = 122°F The highest recorded temperature in Europe is 122°F.

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