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1-1 Evaluating Algebraic Expressions
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
1-1 Evaluating Algebraic Expressions
Warm UpEvaluate.
1. 21 – 2(3) 15
31
21
20.4
15.35. 7(2.9) – 5
4. 6(1.4) + 12
3. 2(9) + (3)
2. 4 + 3 9
1-1 Evaluating Algebraic Expressions
Problem of the Day
Miss Smith obtained the prices below from the landscape company. She plans to buy five birch, two elm, one dogwood, and two oak trees. The landscape company will charge her $15 to plant each tree. How much will it cost?
Trees TreesPrice Price
Maple
Elm
Oak
DogwoodCrab apple
Birch
$16.99
$22.99
$19.99
$23.99
$26.99
$17.99
$337.90
1-1 Evaluating Algebraic Expressions
Learn to evaluate algebraic expressions.
1-1 Evaluating Algebraic Expressions
Vocabularyvariablecoefficientalgebraic expressionconstantevaluatesubstitute
1-1 Evaluating Algebraic Expressions
A variable is a letter that represents a value that can change or vary.
The coefficient is the number multiplied by the variable.
Coefficient Variable
1-1 Evaluating Algebraic Expressions
In the algebraic expression x + 6, 6 is a constant because it does not change.
To evaluate an algebraic expression, substitute a given number for the variable, and find the value of the resulting numerical expression.
An algebraic expression has one or more variables.
1-1 Evaluating Algebraic Expressions
Evaluate each 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
1-1 Evaluating Algebraic Expressions
Order of Operations
PEMDAS: 1. Parentheses 2. Exponents3. Multiply and Divide from left to right.4. Add and Subtract from left to right.
Remember!
1-1 Evaluating Algebraic Expressions
Evaluate each 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
1-1 Evaluating Algebraic Expressions
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
5
6
7
n Substitute Parentheses Multiply Subtract
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
1-1 Evaluating Algebraic Expressions
Evaluate each expression for the given value of the variable.
Check It Out: Examples 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
1-1 Evaluating Algebraic Expressions
Evaluate the expression for the given values of the variable.
Check It Out: Example 1
C. 5(n + 3) – 2 for n = 3, 4, 5
3
4
5
n Substitute Parentheses Multiply Subtract
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
1-1 Evaluating Algebraic Expressions
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
1-1 Evaluating Algebraic Expressions
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
1-1 Evaluating Algebraic Expressions
Use the expression 1.8c + 32 to convert the boiling point temperature from degrees Celsius to degrees Fahrenheit.
Additional Example 3A: Physical Science Application
Substitute 100 for c.
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.
1-1 Evaluating Algebraic Expressions
Additional Example 3B: Physical Science Application
Substitute 85 for c.
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.
1-1 Evaluating Algebraic Expressions
Use the expression 1.8c + 32 to convert the temperature from degrees Celsius to degrees Fahrenheit.
Check It Out: Example 3A
Substitute 50 for c.
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.
1-1 Evaluating Algebraic Expressions
Use the expression 1.8c + 32 to convert the temperature from degrees Celsius to degrees Fahrenheit.
Check It Out: Example 3B
Substitute 10 for c.
Multiply.
10°C
1.8(10) + 32
18 + 32
1.8c + 32
Add.50
10°C = 50°F
1-1 Evaluating Algebraic Expressions
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
1-1 Evaluating Algebraic Expressions
Lesson QuizEvaluate each expression for the given values of the variables.
1. 6x + 9 for x = 3
2. x + 14 for x = 8
3. 4x + 3y for x = 2, y = 3
4. 1.6x – 2.9y for x = 19, y = 6
5. If n is the amount of money in a savings account, then the expression n + 0.03n 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.
27
22
17
13
$515
1-1 Evaluating Algebraic Expressions
1. Evaluate the expression for the given value of the variable.
6x + 12 for x = 7
A. 23
B. 40
C. 54
D. 65
Lesson Quiz for Student Response Systems
1-1 Evaluating Algebraic Expressions
2. Evaluate the expression for the given value of the variable.
k + 72 for k = 7
A. 79
B. 82
C. 96
D. 98
Lesson Quiz for Student Response Systems
1-1 Evaluating Algebraic Expressions
3. Evaluate the expression for the given values of the variables.
2m + 2n for m = 4, n = 5
A. 18
B. 20
C. 22
D. 24
Lesson Quiz for Student Response Systems
1-1 Evaluating Algebraic Expressions
4. Evaluate the expression for the given values of the variables.
3.2r – 4.6s for r = 20, s = 5
A. 30
B. 35
C. 39
D. 41
Lesson Quiz for Student Response Systems
1-1 Evaluating Algebraic Expressions
5. If n is the amount of money that Bill had borrowed from a bank, then the expression n + 0.05n can be used to find the total amount Bill has to return after one year with respect to the interest rate. How much money should Bill pay after one year if $700 is the amount borrowed?
A. $710
B. $717
C. $735
D. $742
Lesson Quiz for Student Response Systems