ObjectiveThe student will be able to:

translate verbal expressions into math expressions and vice versa.

translate verbal expressions into math expressions and vice versa.

What is the area of a rectangle?

Length times Width

If the length is 3 meters and the width is 2 meters, what is the area?

A = L x WA = 3 x 2 = 6 meters2

A, L and W are the variables. It is any letter that represents an unknown number.

An algebraic expression contains:

1) one or more numbers or variables, and

2) one or more arithmetic operations.

Examples:

x - 3

3 • 2n

41

m

In expressions, there are many different ways to write multiplication.

1) ab 2) a • b 3) a(b) or (a)b 4) (a)(b) 5) a x b

We are not going to use the multiplication symbol

any more. Why?

Division, on the other hand, is written as:

1)

2) x ÷ 3

x

3

Throughout this year, you will hear many words that mean addition, subtraction,

multiplication, and division. Complete the table with as many as you know.

Addition Subtraction Multiplication Division

Here are some phrases you may have listed. The terms with * are ones that are often

used.

Addition Subtraction Multiplication Division

sum* difference* product* quotient*

increase decrease times divided

plus minus multiplied ratio

add subtract

more than less than

total

Example 1: Write an algebraic expression for:

a) m increased by 5.

b) 7 times the sum of x and t.

m + 5

7(x + t)

c) 11 less than 4 times a number.

d) two more than 6 times a number.

e) the quotient of a number and 12.

4y - 11

6f + 2

t ÷ 12 or 12

t

Which of the following expressions represents 7 times a number decreased by 13?

1. 7x + 13

2. 7x - 13

3. 13 - 7x

4. 13 + 7x

Which one of the following expressions represents 28 less than three times a number?

1. 28 - 3x

2. 3x - 28

3. 28 + 3x

4. 3x + 28

Example 2: Write a verbal expression for:

a) 8 + a.

Do you have a different way of writing these?

b)

m

r.

Which of the following verbal expressions represents 2x + 9?

1. 9 increased by twice a number

2. a number increased by nine

3. twice a number decreased by 9

4. 9 less than twice a number

Which of the following expressions represents the sum of 16 and five times a number?

1. 5x - 16

2. 16x + 5

3. 16 + 5x

4. 16 - 5x

baseand 3 is called the

exponent.103 means 10 • 10 • 10

103 = 1000

When looking at the expression 103, 10 is called the

How is it said?21

Two to the first power22

Two to the second power or two squared23

Two to the third power or two cubed2n7

Two times n to the seventh power

Which of the following verbal expressions represents x2 + 2x?

1. the sum of a number squared and twice a number

2. the sum of a number and twice the number

3. twice a number less than the number squared

4. the sum of a number and twice the number squared

Which of the following expressions represents four less than the cube of a

number?

1. 4 – x3

2. 4 – 3x

3. 3x – 4

4. x3 – 4

EXAMPLE 3 Find a unit rate

A car travels 110 miles in 2 hours. Find the unit rate.

110 miles 2 hours = 1 hour

55 miles2 hours 2

110 miles 2 =

The unit rate is 55 miles per hour, or 55 mi/h

ANSWER

SOLUTION

Cell Phones

EXAMPLE 4 Solve a multi-step problem

Your basic monthly charge for cell phone service is $30, which includes 300 free minutes. You pay a fee for each extra minute you use. One month you paid $3.75 for 15 extra minutes. Find your total bill if you use 22 extra minutes.

STEP 1 Calculate the unit rate.

153.75

=

0.25

1 = $.25 per minute

EXAMPLE 5 Solve a multi-step problem

Write a verbal model and then an expression. Let m be the number of extra minutes.

STEP 2

30 + 0.25 m

EXAMPLE 5 Solve a multi-step problem

Evaluate the expression when m = 22.

30 + 0.25(22) = 35.5

ANSWER

The total bill is $35.50.

STEP 3