1-4 Variables and Algebraic Expressions

Warm UpWarm Up

Lesson PresentationLesson PresentationProblem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

1-4 Variables and Algebraic Expressions

Warm UpEvaluate.

1. 5(7) – 12. 7(18 – 11)3. 22 + 17 8 + 34. 36 + 15(40 – 35)5. 33 + 7(12 – 4)

3449

16111183

1-4 Variables and Algebraic Expressions

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

1-4 Variables and Algebraic Expressions

Prep for MA.7.A.3.3 Formulate and use different strategies to solve one-step…linear equations…Review MA.6.A.3.1Also Prep for MA.7.A.3.2

Sunshine State Standards

1-4 Variables and Algebraic Expressions

Vocabularyvariableconstantalgebraic expressionevaluate

1-4 Variables and Algebraic Expressions

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.

1-4 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, 1942 + a is an algebraic expression for the year Ron Howard turns a certain age.

1-4 Variables and Algebraic Expressions

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

Age Year born + age = year at age

18 1942 + 18 196025 1942 + 25 196736 1942 + 36 197863 1942 + 63 2005a 1942 + a

1-4 Variables and Algebraic Expressions

Evaluate k + 9 for each value of k.

Additional Example 1: Evaluating Algebraic Expressions

A. k = 5 k + 9

5 + 914

Substitute 5 for k.Add.

B. k = 2 k + 9

2 + 9 Substitute 2 for k.

11 Add.

1-4 Variables and Algebraic ExpressionsCheck It Out: Example 1

Evaluate a + 6 for each value of a.

A. a = 3 a + 6

3 + 69

Substitute 3 for a.

Add.

B. a = 5 a + 6

5 + 6 Substitute 5 for a.

11 Add.

1-4 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.

1-4 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 = 24(2) – 3

8 – 35

Substitute 2 for x.Multiply.Subtract.

1-4 Variables and Algebraic ExpressionsAdditional Example 2: Evaluating Algebraic Expressions

Involving Order of Operations

B. s ÷ 5 + s, for s = 15 15 ÷ 5 + 15

3 + 1518

C. 5x2 + 3x, for x = 2 5(2)2 + 3(2)5(4) + 3(2)

20 + 626

Substitute 15 for s.Divide.Add.

Substitute 2 for x.Evaluate the power.Multiply.Add.

1-4 Variables and Algebraic ExpressionsCheck It Out: Example 2A

Evaluate the expression for the given value of the variable.A. 3x – 2 for x = 3

3(3) – 29 – 2

7

Substitute 3 for x.Multiply.Subtract.

1-4 Variables and Algebraic ExpressionsCheck It Out: Example 2

B. r ÷ 3 + r, for r = 12 12 ÷ 3 + 12

4 + 1216

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.

1-4 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.

1-4 Variables and Algebraic ExpressionsCheck 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.

1-4 Variables and Algebraic Expressions

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

1-4 Variables and Algebraic ExpressionsLesson Quiz

Evaluate 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 = 36. 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

16256x 23

84

1-4 Variables and Algebraic Expressions

1. Evaluate m + 4 for m = 19. A. 21B. 27C. 23D. 28

Lesson Quiz for Student Response Systems

1-4 Variables and Algebraic Expressions

2. Evaluate 7x – 8 for x = 5. A. 20B. 27C. 22D. 32

Lesson Quiz for Student Response Systems

1-4 Variables and Algebraic Expressions

3. Evaluate 6x2 + 5x for x = 5.A. 185B. 85C. 175 D. 50

Lesson Quiz for Student Response Systems

1-4 Variables and Algebraic Expressions

4. Evaluate + 5y for x = 3 and y = 5.A. 38B. 44C. 54D. 64

Lesson Quiz for Student Response Systems

39y

1-4 Variables and Algebraic Expressions

5. The expression 12n gives the number of months in n years. Evaluate 12n for n = 3. How many months are in 3 years?

A. 12 monthsB. 24 monthsC. 36 monthsD. 48 months

Lesson Quiz for Student Response Systems