Course 2

1-7 Variables and Algebraic Expressions1-7 Variables and Algebraic Expressions

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Course 2

1-7 Variables and Algebraic Expressions

Warm UpEvaluate.

1. 5(7) – 1

2. 7(18 – 11)

3. 22 + 17 8 + 3

4. 36 + 15(40 – 35)

5. 33 + 7(12 – 4)

34

49

161

111

83

Course 2

1-7 Variables and Algebraic Expressions

Problem of the Day

If charged per cut, how much will it cost to cut a log into eight pieces if cutting it into four pieces costs $12?$28

Course 2

1-7 Variables and Algebraic Expressions

Learn to evaluate algebraic expressions.

Course 2

1-7 Variables and Algebraic Expressions

Vocabulary

variableconstantalgebraic expressionevaluate

Course 2

1-7 Variables and Algebraic Expressions

Ron Howard was born in 1954. You can find out what year Ron turned 16 by adding the year he was born to his age.

1954 + 16

In algebra, letters are often used to represent numbers. You can use a letter such as a to represent Ron Howard’s age. When he turns a years old, the year will be

1954 + a.

Course 2

1-7 Variables and Algebraic Expressions

The letter a has a value that can change, or vary. When a letter represents a number that can vary, it is called a variable. The year 1954 is a constant because the number cannot change.

An algebraic expression consists of one or more variables. It usually contains constants and operations. For example, 1954 + a is an algebraic expression for the year Ron Howard turns a certain age.

Course 2

1-7 Variables and Algebraic Expressions

To evaluate an algebraic expression, substitute a number for the variable.

Age Year born + age = year at age

16 1954 + 16 1970

18 1954 + 18 1972

21 1954 + 21 1975

36 1954 + 36 1990

a 1954 + a

Course 2

1-7 Variables and Algebraic Expressions

Evaluate k + 9 for each value of k.

Additional Example 1: Evaluating Algebraic Expressions

A. k = 5 k + 9

5 + 9

14

Substitute 5 for k.

Add.

B. k = 2 k + 9

2 + 9 Substitute 2 for k.

11 Add.

Course 2

1-7 Variables and Algebraic Expressions

Check It Out: Example 1

Evaluate a + 6 for each value of a.

A. a = 3 a + 6

3 + 6

9

Substitute 3 for a.

Add.

B. a = 5 a + 6

5 + 6 Substitute 5 for a.

11 Add.

Course 2

1-7 Variables and Algebraic Expressions

Multiplication and division of variables can be written in several ways, as shown in the table.

When evaluating expressions, use the order of operations.

Course 2

1-7 Variables and Algebraic Expressions

Evaluate the expression for the given value of the variable.

Additional Example 2: Evaluating Algebraic Expressions Involving Order of Operations

A. 4x – 3 for x = 2

4(2) – 3

8 – 3

5

Substitute 2 for x.

Multiply.

Subtract.

Course 2

1-7 Variables and Algebraic Expressions

Additional Example 2: Evaluating Algebraic Expressions Involving Order of Operations

B. s ÷ 5 + s, for s = 15

15 ÷ 5 + 15

3 + 15

18

C. 5x2 + 3x, for x = 2

5(2)2 + 3(2)

5(4) + 3(2)

20 + 6

26

Substitute 15 for s.

Divide.

Add.

Substitute 2 for x.

Evaluate the power.

Multiply.

Add.

Course 2

1-7 Variables and Algebraic Expressions

Check It Out: Example 2A

Evaluate the expression for the given value of the variable.

A. 3x – 2 for x = 3

3(3) – 2

9 – 2

7

Substitute 3 for x.

Multiply.

Subtract.

Course 2

1-7 Variables and Algebraic Expressions

Check It Out: Example 2

B. r ÷ 3 + r, for r = 12

12 ÷ 3 + 12

4 + 12

16

C. 4y2 + 2y, for y = 3

4(3)2 + 2(3)

4(9) + 2(3)

36 + 642

Substitute 12 for r.

Divide.

Add.

Substitute 3 for y.

Evaluate the power.

Multiply.Add.

Course 2

1-7 Variables and Algebraic Expressions

Evaluate

Additional Example 3: Evaluating Algebraic Expressions with Two Variables

6a + 4b, for a = 3 and b = 2.

6a + 4b

63 + 4(2)

2 + 8

10

Substitute 3 for a and 2 for b.

Divide and multiply from left to right.

Add.

Course 2

1-7 Variables and Algebraic Expressions

Check It Out: Example 3

Evaluate 8w + 2x, for w = 4 and x = 2.

8w + 2x

84 + 2(2)

2 + 4

6

Substitute 4 for w and 2 for x.

Divide and multiply from left to right.

Add.

Course 2

1-7 Variables and Algebraic Expressions

Lesson QuizEvaluate n + 7 for each value of n.

1. n = 25 2. n =31

Evaluate each algebraic expression for the given value of the variables

3. 6y – 5 for y = 7

4. 4x2 + 3x for x = 6

5. + 3y for x = 4 and y = 3

6. The expression 7d gives the number of days in d weeks. Evaluate 7d for d = 12. How many days are in 12 weeks?

3832

37

162

56x 23

84