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1-1. Variables and Expressions. Warm Up. Problem of the Day. Lesson Presentation. Course 3. 1-1. Variables and Expressions. Course 3. Warm Up Evaluate. 1. 21  2(3). 15. 2. 4 + 3  9. 31. 3. 2(9) + (3). 21. 4. 6(1.4) + 12. 20.4. 5. 7(2.9)  5 . 15.3. 1-1.

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slide1

1-1

Variables and Expressions

Warm Up

Problem of the Day

Lesson Presentation

Course 3

slide2

1-1

Variables and Expressions

Course 3

Warm Up

Evaluate.

1. 21  2(3)

15

2. 4 + 3  9

31

3. 2(9) + (3)

21

4. 6(1.4) + 12

20.4

5. 7(2.9)  5

15.3

slide3

1-1

Variables and Expressions

Price

Trees

Price

Trees

$23.99

Dogwood

$22.99

Maple

Elm

$16.99

$26.99

Crab apple

$19.99

$17.99

Birch

Oak

Course 3

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?

$337.90

slide4

1-1

Variables and Expressions

Course 3

Learn to evaluate algebraic expressions.

slide5

1-1

Variables and Expressions

Course 3

Vocabulary

variable

coefficient

algebraic expression

constant

evaluate

substitute

slide6

1-1

Variables and Expressions

Course 3

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

slide7

1-1

Variables and Expressions

Course 3

An algebraic expression has one or more variables.

In the algebraic expression x + 6, 6 is a constantbecause 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.

slide8

1-1

Variables and Expressions

Course 3

Additional Examples 1A and 1B: Evaluating Algebraic Expressions with One Variable

Evaluate each expression for the given value of the variable.

A.x – 5 for x = 12

12– 5

Substitute 12 for x.

7

Subtract.

B.2y + 1 for y = 4

2(4) + 1

Substitute 4 for y.

8 + 1

Multiply.

9

Add.

slide9

1-1

Variables and Expressions

n Substitute Parentheses Multiply Subtract

5

6

7

Course 3

Additional Example 1C: Evaluating Algebraic Expressions with One Variable

Evaluate the expression for the given values of the variable.

C.6(n + 2) – 4 for n = 5, 6, 7

6(5 + 2) – 4

6(7) – 4

38

42 – 4

6(6 + 2) – 4

6(8) – 4

44

48 – 4

6(7 + 2) – 4

6(9) – 4

50

54 – 4

slide10

1-1

Variables and Expressions

Course 3

Try This: Examples 1A and 1B

Evaluate each expression for the given value 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.

slide11

1-1

Variables and Expressions

n Substitute Parentheses Multiply Subtract

3

4

5

Course 3

Try This: Example 1C

Evaluate the expression for the given values of the variable.

C.5(n + 3) – 2 for n = 3, 4, 5

5(3 + 3) – 2

5(6) – 2

28

30 – 2

5(4 + 3) – 2

5(7) – 2

33

35 – 2

5(5 + 3) – 2

5(8) – 2

38

40 – 2

slide12

1-1

Variables and Expressions

Course 3

Additional Example 2: Evaluating Algebraic Expressions with Two Variables

Evaluate each expression for the given value 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.8.5 r – 2p for r = 2 and p = 5.5

8.5(2) – 2(5.5)

Substitute 2 for r and 5.5 for p.

17 – 11

Multiply.

6

Subtract.

slide13

1-1

Variables and Expressions

Course 3

Try This: Example 2

Evaluate each expression for the given value 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 – 3.5r for q = 2.5 and r = 2

8(2.5) – 3.5(2)

Substitute 2.5 for q and 2 for r.

20 – 7

Multiply.

13

Subtract.

slide14

1-1

Variables and Expressions

Course 3

Additional Example 3A: Physical Science Application

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

A.Boiling point of water at sea level: 100°C

1.8c + 32

1.8(100) + 32

Substitute 100 for c.

180 + 32

Multiply.

212

Add.

100°C = 212°F

Water boils at 212°F.

slide15

1-1

Variables and Expressions

Course 3

Additional Example 3B: Physical Science Application

Convert the temperature from degrees Celsius to degrees Fahrenheit.

B.Antarctica’s highest recorded temperature (Vanda Station, Scott Coast): 15°C

1.8c + 32

1.8(15) + 32

Substitute 15 for c.

27 + 32

Multiply.

59

Add.

15°C = 59°F

The highest recorded temperature in Antarctica is 59°F.

slide16

1-1

Variables and Expressions

Course 3

Try This: Example 3A

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

A.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.

slide17

1-1

Variables and Expressions

Course 3

Try This: Example 3B

Convert the temperature from degrees Celsius to degrees Fahrenheit.

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

1.8c + 32

1.8(50) + 32

Substitute 50 for c.

90 + 32

Multiply.

122

Add.

50°C = 122°F

The highest recorded temperature in Europe is 122°F.

slide18

1-1

Variables and Expressions

Course 3

Lesson Quiz

Evaluate 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