1.1 Variables and Expressions

1
1.1 Variables and Expressions

• Students will translate verbal expressions
  into algebraic expressions and vice versa.
• Key Vocabulary
• Variable symbol used to represent unspecified
  numbers or values
• Algebraic expression consists of one or more
  numbers and variables along with one or more
  arithmetic operations
• Evaluate to find an expressions value

Designed by Skip Tyler, Edited by Diane Warren
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
An algebraic expression contains

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

4
In expressions, there are many different ways to
write multiplication.

• 1) ab
• 2) a b
• 3) a(b) or (a)b
• 4) (a)(b)
• We are not going to use the multiplication symbol
  any more so the times sign will not be confused
  with the variable x.

5
Division, on the other hand, is written as

• 1)
• 2) x 3

6
Throughout this year, you will hear many words
that mean addition, subtraction, multiplication,
and division. The table lists some of the most
common.
7
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

8
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.
9
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

10
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

11
Write a verbal expression for 1) 8 a.
The sum of 8 and a
The ratio of m to r There are other
possible ways.
12
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

13
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

14
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

15
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

16
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

17
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

18
Evaluate.21

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

19
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!