ObjectiveThe student will be able to:

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.

VOCABULARYA numerical expression is a mathematical phrase with only numbers and operation symbols (+, -, x, ÷).

Example: 8 + 5 - 2

An algebraic expression is a mathematical phrase that contains a variable and operation symbols.

A variable is a symbol (usually a letter) that stands for a number.

Algebraic expression: 5y + 2

Evaluating Algebraic Expressions

• Replace the variable with the value that you are given.

• Now we have a numerical expression.

• Solve using order of operations.

Example: Evaluate 2b-8 for b=11

2b-8Substitute the 11 for the variable.2(11)-8Multiplying comes before subtracting.22 - 8

14

An algebraic expression contains:

1) one or more numbers or variables, and

2) one or more arithmetic operations.

Examples:

x - 3

3 • 2n4

1m

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 twice half

more than less than doubled a third

total

Write an algebraic expression for

1) m increased by 5.m + 5

2) 7 times the product of x and t.

7xt or 7(x)(t) or 7 • x • t

3) 11 less than 4 times a number.

4n - 11

4) two more than 6 times a number.

6n + 2

5) the quotient of a number and 12.

12

x

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

Answer NowAnswer Now

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

Answer NowAnswer Now

Write a verbal expression for:

1) 8 + a.

The ratio of m to rDo you have a different way of writing these?

The sum of 8 and a

2)

m

r.

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

Answer NowAnswer Now

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?

Answer NowAnswer Now

1. 5x - 16

2. 16x + 5

3. 16 + 5x

4. 16 - 5x

baseand 3 is called the

exponent or power.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?

Answer NowAnswer Now

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?

Answer NowAnswer Now

1. 4 – x3

2. 4 – 3x

3. 3x – 4

4. x3 – 4

Evaluate.21

222

2 • 2 = 423

2 • 2 • 2 = 82n7

We can’t evaluate because we don’t know what n equals to!!

Is 35 the same as 53?Evaluate each and find out!

35 = 3 • 3 • 3 • 3 • 3 = 24353 = 5 • 5 • 5 = 125

243 ≠ 125 They are not the same!

Translate each verbal expressions into an algebraic expression:

(a)the sum of 8 and y

(b) 4 less than x

(c) a number decreased by one

(d) The difference between x and y

(e) One half of a

(f) Nine less than the total of 9 and a number

8 + y

x - 4

n - 1

x - y

½ a

(9 + n)- 9

Write an algebraic expression to describe Jerry’s age. Use the following information:

Jerry is 4 years younger than his brother Steve.

First, we have to know how old Steve is. We do not have an age for Steve, soFirst, we have to know how old Steve is. We do not have an age for Steve, so we will use a variable:

Let s = Steve’s age

Now that we have determined Steve’s age (s), we can use it to determine Jerry’s age. Jerry is 4 years younger than Steve.

j = s - 4

If Steve is 22 years old, then how old is Jerry?

j = s – 4

j = 22 - 4

j = 18Jerry is 18 years old.