Objective The student will be able to:

1
ObjectiveThe student will be able to

• translate verbal expressions into math
  expressions and vice versa.

2
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.

3
VOCABULARY
A 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
4
Evaluating Algebraic Expressions

• Replace the variable with the value that you are
  given.
• Now we have a numerical expression.
• Solve using order of operations.

5
Example Evaluate 2b-8 for b11
2b-8
2(11)-8
Substitute the 11 for the variable.
22 - 8
Multiplying comes before subtracting.
14
6
An algebraic expression contains

• 1) one or more numbers or variables, and
• 2) one or more arithmetic operations.
• Examples
• x - 3
• 3 2n

7
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?

8
Division, on the other hand, is written as

• 1)
• 2) x 3

9
Throughout this year, you will hear many words
that mean addition, subtraction, multiplication,
and division. Complete the table with as many as
you know.
10
Here are some phrases you may have listed. The
terms with are ones that are often used.
11
Write an algebraic expression for1) m increased
by 5.

• m 5
• 2) 7 times the product of x and t.
• 7xt or 7(x)(t) or 7 x t

12
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.
13
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

14
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

15
Write a verbal expression for 1) 8 a.
The sum of 8 and a
The ratio of m to r Do you have
a different way of writing these?
16
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

17
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

18
When looking at the expression 103, 10 is called
the

• base
• and 3 is called the
• exponent or power.
• 103 means 10 10 10
• 103 1000

19
How is it said?21

• Two to the first power
• 22
• Two to the second power or two squared
• 23
• Two to the third power or two cubed
• 2n7
• Two times n to the seventh power

20
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

21
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

22
Evaluate.21

• 2
• 22
• 2 2 4
• 23
• 2 2 2 8
• 2n7
• We cant evaluate because we dont know what n
  equals to!!

23
Is 35 the same as 53?Evaluate each and find out!

• 35 3  3 3 3 3 243
• 53 5 5 5 125
• 243 ? 125
• They are not the same!

24

• Translate each verbal expressions into an
  algebraic expression
• 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
25
Write an algebraic expression to describe Jerrys
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 Steves
age
Now that we have determined Steves age (s), we
can use it to determine Jerrys age. Jerry is 4
years younger than Steve.
j s - 4
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If Steve is 22 years old, then how old is Jerry?
j s 4
j 22 - 4
Jerry is 18 years old.
j 18