This document defines key terms related to algebraic expressions. It explains that an algebraic expression contains at least one variable, operation, and constant. A variable represents an unknown value and can be any letter. Terms are the parts of an expression that are added or subtracted, like 5x or 6. Constants do not change value. Coefficients are numbers multiplied by variables. The document provides examples of evaluating simple expressions by substituting values for variables.

2. What is Expressions

3. Expressions
You are familiar with the following
type of numerical expressions:
12+6
3 (12)
6 (3 + 2)
15 - 4 (6)

4. Definitions
• Algebraic expression – an
expression that contains at least
one variable, operation, and
constant
• m + 8
• r – 3

5. What is a variable?
In the expression 12 + B, the letter “B”
is a variable.
A variable is a letter or symbol that
represents an unknown value.

6. Definitions
• Variable – A variable is a letter
or symbol that represents a
number (unknown quantity).
• 8 + n = 12

7. Definitions
• A variable can use any letter of
the alphabet. (expect o and
needs to be lower case)
• n + 5
• x – 7
• w - 25

8. Algebraic Expressions
When variables are used with other
numbers, parentheses, or operations, they
create an algebraic expression.
a + 2
(a) (b)
3m + 6n - 6

9. What are coefficients?
A coefficient is the number multiplied
by the variable in an algebraic
expression.
Algebraic Expression Coefficient
6m + 5 6
8r + 7m + 4 8, 7
14b - 8 14

10. What is a term?
A term is the name given to a number, a
variable, or a number and a variable
combined by multiplication or division.
Algebraic Expressions Terms
a + 2 a, 2
3m + 6n - 6 3m, 6n, - 6

11. What are constants?
 A constant is a number that cannot
change its value.
In the expression: 5x + 7y - 2
the constant is - 2.

12. Definitions
• A constant is a number that does not
change.
• A coefficient is a number multiplied or
divided by a variable.
6x + 5
6 is the coefficient, x is the variable, and 5 is
the constant.

13. Definitions
• A term is a part of an expression that are
added or subtracted
5x + 6 – 4x
This expression has 3 terms: 5x, 6, and 4x
• A like term are terms who have the same
variable raised to the same power
In the expression above, 5x and 4x are like
terms

14. Which is the variable in the term
215pq?
A.
B.
C.
D.
215
p
Pq
215pq

15. Determine the constant and the
variable
2a
X+3
2f+5
-3(m+n)
-3c

16. Definitions
• Evaluate an algebraic expression –
To find the value of an algebraic
expression substitute numbers for
variables and simplify.
• m + 8 m = 2 2 + 8 = 10
• r – 3 r = 5 5 – 3 = 2

17. Which is the coefficient in the term
11mn?
A.
B.
C.
D.
m
n
11
m,n

18. Definitions
• Simplify – Combine like terms
and complete all operations
m = 2
• m + 8 + m 2 m + 8
• (2 x 2) + 8 4 + 8 = 12

19. Words That Lead to Addition
• Sum
• More than
• Increased
• Plus
• Altogether

20. Words That Lead to Subtraction
• Decreased
• Less
• Difference
• Minus
• How many more

21. Write Algebraic Expressions
for These Word Phrases
• Ten more than a number
• A number decrease by 5
• 6 less than a number
• A number increased by 8
• The sum of a number & 9
• 4 more than a number
n + 10
w - 5
x - 6
n + 8
n + 9
y + 4

22. Write Algebraic Expressions
for These Word Phrases
• A number s plus 2
• A number decrease by 1
• 31 less than a number
• A number b increased by 7
• The sum of a number & 6
• 9 more than a number
s + 2
k - 1
x - 31
b + 7
n + 6
z + 9

23. Evaluate each algebraic
expression when x = 10
• x + 8
• x + 49
• x + x
• x - x
• x - 7
• 42 - x
18
59
20
0
3
32

24. Complete This Table
n n - 3
5
10
21
32
2
7
18
29

25. Complete This Table
x x + 6
5
10
21
32
11
16
27
38

26. Write an Algebraic Expression
for These Situations
• Scott’s brother is 2 years younger than
Scott
• The sum of two numbers is 12
• The difference between two numbers is 5
s - 2
v + c = 12
m – n = 5