1. 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

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.
Numerical Expressions
Algebraic Expressions
(5)
27 – 18
x n
p – r

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

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 n
Substitute
Parentheses
Multiply
Subtract 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

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 n
Substitute
Parentheses
Multiply
Subtract 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.
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 t meters: 85°C
1.8c + 32
1.8(85) + 32
Substitute 85 for c.
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.
Multiply.
122
Add.
50°C = 122°F
The highest recorded temperature in Europe is 122°F.