This document provides examples and explanations of key concepts for translating between verbal and algebraic expressions, including: 1) Definitions of variables, expressions, operations like addition, subtraction, multiplication and division. 2) Examples of writing algebraic expressions to represent verbal phrases like "7 times a number decreased by 13" and vice versa. 3) Explanations of exponents and powers, and examples of evaluating expressions like 21, 22, 23, and 2n7. 4) Practice identifying equivalent expressions and evaluating whether expressions are equal, like 35 and 53.

1. Objective
The student will be able to:
translate verbal expressions into
math expressions and vice versa.
SOL: A.1
Designed by Skip Tyler, Varina High School

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 W
A = 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
1
m
+

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)
5) a x b
We are not going to use the multiplication symbol
any more. Why?

5. Division, on the other hand, is
written as:
1)
2) x ÷ 3
x
3

6. 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

7. 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

8. 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

9. 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

10. 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 Now

11. 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 Now

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

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

14. Which of the following expressions represents
the sum of 16 and five times a number?
Answer Now
1. 5x - 16
2. 16x + 5
3. 16 + 5x
4. 16 - 5x

15. base
and 3 is called the
exponent or power.
103
means 10 • 10 • 10
103
= 1000
When looking at the expression
103
, 10 is called the

16. 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

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

18. Which of the following expressions
represents four less than the cube of a
number?
Answer Now
1. 4 – x3
2. 4 – 3x
3. 3x – 4
4. x3
– 4

19. Evaluate.
21
2
22
2 • 2 = 4
23
2 • 2 • 2 = 8
2n7
We can’t evaluate because we don’t
know what n equals to!!

20. 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!