evaluating algebraic expressions 1-1 af1.2 use the correct order of operations to evaluate algebraic...

Evaluating Algebraic Expressions


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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.

California Standards



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Vocabularyexpressionvariablenumerical expressionalgebraic expressionevaluate



1-1An 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.

Numerical Expressions Algebraic Expressions

3 + 2 4(5)

27 – 18

x + 2 4n

p – r



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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.



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Evaluate the expression for the given value of the variable.

Additional Example 1A: Evaluating Algebraic Expressions with One Variable

Substitute 12 for x.

Subtract.

x – 5 for x = 12

12 – 5

7



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Order of Operations

PEMDAS: 1. Parentheses 2. Exponents3. Multiply and Divide from left to right.4. Add and Subtract from left to right.

Remember!



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Evaluate the expression for the given value of the variable.

Additional Example 1B: Evaluating Algebraic Expressions with One Variable

Substitute 4 for y.

Multiply.

2y + 1 for y = 4

2(4) + 1

8 + 1

Add.9



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Evaluate the expression for the given values of the variable.

Additional Example 1C: Evaluating Algebraic Expressions with One Variable

6(n + 2) – 4 for n = 5, 6, 7

6(5 + 2) – 4 6(7) – 4 42 – 4 38

6(6 + 2) – 4 6(8) – 4 48 – 4 44

6(7 + 2) – 4 6(9) – 4 54 – 4 50

n Substitute Parentheses Multiply Subtract

5

6

7



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Evaluate each expression for the given values of the variable.

Check It Out! Example 1

Substitute 3 for x.

Add.

A. x + 5 for x = 3

3 + 5

8

Substitute 11 for c.

Multiply.

B. 4c + 1 for c = 11

4(11) + 1

44 + 1

Add.45



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Evaluate the expression for the given values of the variable.

Check It Out! Example 1C

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

n Substitute Parentheses Multiply Subtract

3

4

5



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Evaluate each expression for the given values of the variables.

Additional Example 2: Evaluating Algebraic Expressions with Two Variables

Substitute 2 for x and 1 for y.

Multiply.

A. 4x + 3y for x = 2 and y = 1

4(2) + 3(1)

8 + 3

Substitute 3 for r and 5 for p.

Multiply.

B. 9r – 2p for r = 3 and p = 5

9(3) – 2(5)

27 – 10

Add.11

Subtract.17



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Evaluate each expression for the given values of the variables.

Check It Out! Example 2

Substitute 3 for x and 4 for y.

Multiply.

A. 3x + 2y for x = 3 and y = 4

3(3) + 2(4)

9 + 8

Substitute 2 for q and 2 for r.

Multiply.

B. 8q – 3r for q = 2 and r = 2

8(2) – 3(2)

16 – 6

Add.17

Subtract.10



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Use the expression 1.8c + 32 to convert the temperature from degrees Celsius to degrees Fahrenheit.

Additional Example 3A: Physical Science Application


Multiply.

Boiling point of water at sea level: 100°C

1.8(100) + 32

180 + 32

1.8c + 32

Add.212

100°C = 212°F

Water boils at 212°F at sea level.



1-1Additional Example 3B: Physical Science Application


Multiply.

Boiling point of water at an altitude of 4400 t meters: 85°C

1.8(85) + 32

153 + 32

1.8c + 32

Add.185

85°C = 185°F

Water boils at 185°F at 4400 m.

Use the expression 1.8c + 32 to convert the temperature from degrees Celsius to degrees Fahrenheit.



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Convert the temperature from degrees Celsius to degrees Fahrenheit.

Check It Out! Example 3A


Multiply.

Europe’s highest recorded temperature (Seville, Spain): 50°C

1.8(50) + 32

90 + 32

1.8c + 32

Add.122

50°C = 122°F

The highest recorded temperature in Europe is 122°F.

evaluating algebraic expressions 1-1 af1.2 use the correct order of operations to evaluate algebraic...

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