This document defines and provides examples of key terms in algebraic expressions including variables, coefficients, constants, factors, and algebraic expressions. It explains that variables represent unknown quantities, coefficients are the numbers in front of terms with variables, and constants contain only numbers. Factors are numbers and/or variables being multiplied together. Algebraic expressions contain at least one variable but no equal sign. Word problems can be written as algebraic expressions using words that lead to addition, subtraction, multiplication, or division. Several examples of writing and evaluating algebraic expressions are provided.

1. Algebraic
Expressions

2. Variable – is a letter or
symbol that represents
an unknown quantity.
X y Z n t

3. COEFFICIENTS
• Coefficients are the number part in front of
the terms with variables.
• Identify the coefficient of the term 3x2.

4. CONSTANTS
• Constants are the terms in the algebraic
expression that contain only numbers (or no
variables).
• Identify the constant in the expression
3x2 + 4y – 2xy + 7.

5. FACTORS
• Factors are numbers and/or variables that
are being multiplied together.
• For example, there are 3 factors in the term
4xy.

6. Algebraic expression-
contains at least one
variable and does not
contain an equal sign
EX: T + 3

7. Since an algebraic expression
contains a variable, we can
evaluate the expression if we
are given what the variable
equals.
If m = 8,
solve the
expression
m + 5.
m + 5
8 + 5
13

8. You can use algebraic expressions
to explain a relationship between
quantities.
Ex: Ashley math grade decreased
by 6 points. Let g represent the
math grade.
g - 6

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

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

11. Words That Lead to Multiplication
• Product
• Total
• Area
• Times
• Of

12. Words That Lead to Division
• Share
• Distribute
• Quotient
• Average

13. Practice Problems
1. Five plus y
2. 6 times q
3. 2 less than x
SEE
ANSWERS

14. ANSWERS
1. 5 + y
2. 6q
3. x - 2

15. Practice Problems
4. Evaluate 7y
when y =2.
5. Evaluate 6 – w
when w = 1.
SEE
ANSWERS

16. ANSWERS
4. 14
5. 5

17. 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

18. 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

19. 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

20. Practice Problems
6. A cake will serve 12
people. Write an
expression for how many
people will C cakes
serve?

21. ANSWERS
6. 12c

22. Practice Problems
7.The drama club sold 60 more
tickets on Saturday as on
Friday (f). Write an
expression for the number of
tickets sold on Saturday.

23. ANSWERS
7. f + 60

24. The End

25. Thank you