1-1 Evaluating Algebraic Expressions
Evaluating
Algebraic Expressions
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.
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
4n
1-1 Evaluating Algebraic Expressions
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 1A: 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
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 1B: Evaluating Algebraic
Expressions with One Variable
Evaluating Algebraic Expressions
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.
1-1 Evaluating Algebraic Expressions
Additional Example 1C: 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
6(5 + 2) – 4
6(7) – 4
6
6(6 + 2) – 4
7
6(7 + 2) – 4
Multiply
Subtract
42 – 4
38
6(8) – 4
48 – 4
44
6(9) – 4
54 – 4
50
1-1 Evaluating Algebraic Expressions
Check It Out! Example 1
Evaluating
Algebraic
Evaluate
each expression
for theExpressions
given values
of the variable.
A. x + 5 for x = 3
3+5
8
Substitute 3 for x.
Add.
B. 4c + 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 1C
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. 4x + 3y for x = 2 and y = 1
4(2) + 3(1)
Substitute 2 for x and 1 for y.
Multiply.
8+3
Add.
11
B. 9r – 2p 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. 3x + 2y for x = 3 and y = 4
3(3) + 2(4)
9+8
17
Substitute 3 for x and 4 for y.
Multiply.
Add.
B. 8q – 3r for q = 2 and r = 2
Substitute 2 for q and 2 for r.
8(2) – 3(2)
Multiply.
16 – 6
10
Subtract.
1-1 Evaluating Algebraic Expressions
Additional Example 3A: Physical Science Application
Use the
expressionAlgebraic
1.8c + 32 to Expressions
convert the
Evaluating
temperature from degrees Celsius to degrees
Fahrenheit.
Boiling point of water at sea level: 100°C
1.8c + 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 3B: Physical Science Application
Use the expression 1.8c + 32 to convert the
temperature
fromAlgebraic
degrees Celsius
to degrees
Evaluating
Expressions
Fahrenheit.
Boiling point of water at an altitude of 4400
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.
t
1-1 Evaluating Algebraic Expressions
Check It Out! Example 3A
Convert the temperature from degrees Celsius
Evaluating
Algebraic Expressions
to degrees
Fahrenheit.
Europe’s highest recorded temperature
(Seville, Spain): 50°C
1.8c + 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.