POD#2basic advanced

2+ 4 × 5 − 32 = (4 + 23 × 4) − 12 =

24

(4 + 8 × 4) − 12

(4 +32) − 12

(36) − 12

2+ 4 × 5 − 9

2+ 20− 9

22− 9

13

Algebraic ExpressionsA variable is a symbol that represents an unknown quantity. An algebraic expression, such as n+2, is an expression that contains variables, numbers, and at least one operation.

The branch of mathematics that involves expressions with variables is called algebra.

The numerical factor of a multiplication expression that contains a variable is called a coefficient. So, 6 is the coefficient of 6d.

6d 9st mn a3

6 times d 9 times s times t m times n a times a times a

Example 1

Evaluate 2(n+3) if n= -4

2(n+3) = 2(-4+3)

=2(-1)

=-2

To translate a verbal phrase into an algebraic expression, the first step is to define a variable. When you define a variable, you choose a variable to represent an unknown quantity.

Example:

Leah has already read 20 pages of a book. She plans to read 5 pages each day from now on. Write an expression that represents the total number of pages she will have read in d days.

20 + 5d

Whiteboard time

Evaluate 8w − 2v if w=5 and v=3

8(5) − 2(3)

40 − 6 34

Evaluate 4y3 + 2 if y=3

4(3)3 + 2

4(27) + 2 108 +2110

An MP3 player costs $70 and song downloads cost $0.85 each. Write an expression that represents the cost of the MP3 player and x number of downloaded songs. Then find the total cost if 20 songs are downloaded.

70 + 0.85x 70 + 0.85 (20) = $87

POD #3basic advanced

3 + 3 × 32 = (4 + 8 ÷ 2)2 − 30 =

34

(4 + 4)2 − 30

(8)2 − 30

64 − 30

3+ 3 × 9

3 + 27

30

Jenny earns $30 a day working part time at a supermarket. Write an algebraic expression to represent the amount of money she will earn in d days.

Let’s practice

30d

A small company has $1000 to distribute to its employees as a bonus. How much money will each employee get? Let e represent the number of employees in the company.

Let’s practice

1000 e

An electrician charges $45 per hour and spends $20 a day on gasoline. Write an algebraic expression to represent his earnings for one day. Let x represent the number of hours the electrician works in one day.

Let’s practice

45x − 20

Fifteen less than twice a number

Let’s practice

2x − 15

Three times a number, increased by seventeen

Let’s practice

3x + 17

The product of nine and a number, decreased by six

Let’s practice

9x − 6