1-1 evaluating algebraic expressions warm up warm up lesson presentation lesson presentation problem...

1-1 Evaluating Algebraic Expressions

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


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


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


Learn to evaluate algebraic expressions.


Vocabularyvariablecoefficientalgebraic expressionconstantevaluatesubstitute


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


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.


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


Order of Operations

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

Remember!



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


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



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


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


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


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


Use the expression 1.8c + 32 to convert the boiling point 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.


Additional 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.

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.


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

Check It Out: Example 3B


Multiply.

10°C

1.8(10) + 32

18 + 32

1.8c + 32

Add.50

10°C = 50°F


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


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. Evaluate the expression for the given value of the variable.

6x + 12 for x = 7

A. 23

B. 40

C. 54

D. 65



2. Evaluate the expression for the given value of the variable.

k + 72 for k = 7

A. 79

B. 82

C. 96

D. 98



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



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



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


1-1 evaluating algebraic expressions warm up warm up lesson presentation lesson presentation problem...

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