1-6 Variables and Algebraic Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson

1-6 Variables and Algebraic Expressions

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

Objective: Students evaluate 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


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


Learn to evaluate algebraic expressions.


Vocabulary

variableconstantalgebraic expressionevaluate


Harrison Ford was born in 1942. You can find out what year Harrison turned 18 by adding the year he was born to his age.

1942 + 18

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

1942 + a.


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, 1942 + a is an algebraic expression for the year Ron Howard turns a certain age.


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


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.


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.


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

When evaluating expressions, use the order of operations.


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.


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.


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.



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.


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.



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.


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


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

Documents

1-6 Variables and Algebraic Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson