1. 1.3 Algebraic Expressions and Terms

2. You are familiar with the following type of numerical expressions:
3 (12)
6 ( )
(6)

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

4. Definitions A variable can use any letter of the alphabet. n + 5 x – 7
w - 25

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

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

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

8. 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 a, 2
3m + 6n m, 6n, - 6

9. Figure it out!
Identify the terms, coefficients, and constants a - 6b x - 2y 3. c x + 2
Terms Coefficients Constants

10. Evaluate m + 8 m = 2 2 + 8 = 10 r – 3 r = 5 5 – 3 = 2
Evaluate an algebraic expression – To find the value of an algebraic expression by substituting numbers for variables.
m + 8 m = = 10
r – 3 r = 5 5 – 3 = 2

11. Simplify m + 8 + m = 2 m + 8 (2 x 2) + 8 4 + 8 = 12 m = 2
Simplifying Algebraic Expression – Combine like terms and complete all operations
m = 2
m m
= 2 m + 8
(2 x 2) = 12

12. Solving Algebraic Expression
When solving real-world problems, you will need to translate words, or verbal expressions, into algebraic expressions.

13. 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

14. Key words to look for: Addition: Subtraction: Add Minus Plus
Sum
Total
Increased by
More than
Subtraction:
Minus
Difference
Subtract
Less than
Decreased by
less

15. Cont… Multiplication Product Times Multiply Double Of for Division
Quotient
Divide
Divided by
Splite by

16. Write algebraic expressions for these word phrases
Four more than s
The product of 7 and c
Nine less than x
A number divided by the sum of 4 and 7.
S+4
7 c
X-9
x/(4+7)

17. Write algebraic expressions for these word phrases
Twice the sum of a number plus 4.
The sum of ¾ of a number and 7.
Ten times a number increased by 150.

18. Write an algebraic phrase for these situations
The plumber double her bill.
Thirty-five fewer people came than the number expected.
2 x b = 2b
X-25

19. Evaluate each algebraic expression when x = 10
x + x
x - x
x - 7
42 - x 18 59 20 3 32

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