1. Algebra 1 Glencoe McGraw-Hill Malinda Young
Variables and Expressions
Order of Operations
Algebra Glencoe McGraw-Hill Malinda Young

2. A VARIABLE is a letter used to represent one or more numbers.
--These numbers are called VALUES of the variable.
--An algebraic expression consists of one or more numbers and variables, along with one or more arithmetic operations..
Examples:
8x y – 2m a(b) x + 6
--Algebraic expressions don’t have equal signs or inequality signs.

3. In algebraic expressions, a dot or a set of parentheses are often used to indicate multiplication. The multiplication symbol of “X” used in arithmetic could be easily mistaken for the variable x. To avoid this confusion, “X” is never used to indicate multiplication in algebra. Here are acceptable ways to represent the product of x and y: xy
Use good form! Variables that are multiplied together should be in alphabetical order.
In each expression, the quantities being multiplied are called factors, and the result is called the product.

4. Exponents and Powers
An expression such as 46 consists of two parts. 46
6 is the exponent
4 is the base
Together, they’re called a POWER.
46 means 4•4•4•4•4•4
46 is read “4 to the sixth power”

5. An exponent applies only to what is directly in front of it!
Look just to the left of the exponent to identify the base of the power.
2x5
x is directly to the left of the exponent. x is the base, not 2x.

6. An exponent applies only to what is directly in front of it!
Look just to the left of the exponent to identify the base of the power.
The right parentheses is directly to the left of the exponent. That means the exponent applies to everything within the parentheses.
(2x)5
32x5

7. Translating Verbal Phrases Into Algebraic Expressions
verbal phrase algebraic expression
the sum of a number and 11
eight more than a number
a number increased by 9
the difference of 2 and a number
five less than a number
seven minus a number
a number less fifteen
x + 11
x + 8
n + 9
2 - x
x - 5
7 - n
z - 15

8. verbal phrase algebraic expression
the product of 6 and a number 6z
10m 3y
ten times a number
a number multiplied by 3
the quotient of a number and four
four divided by a number

9. Write the phrase as an algebraic expression.
a. 9 greater than a number
n + 9
b. a number subtracted from 11
11 – n
c. The sum of a number and 33
n + 33
d. Charlotte’s age minus 27
a – 27 18 n
e. The quotient of 18 and a number
The sum of a number and ten,
divided by two.

10. Translating More Complex Verbal Phrases
“Six more than twice a number” can be written as……
2n + 6
“Eleven less than the sum of a number and 9” can be written as ……
(n + 9) – 11
“Eight decreased by five times a number” can be written as......
8 – 5n
“Nine times the difference of a number and six” can be written as……
9(x – 6)

11. ****IMPORTANT**** Order matters in subtraction!!
“four less than a number” is written x – 4,
NOT 4 – x
“the difference of a number and 1” is written as x – 1,
NOT 1 – x
** Order also matters in division!!**
“the quotient of a number and 12” is written as
“the quotient of 12 and a number” is written as

12. Evaluating Expressions
--When all the variables in an algebraic
expression are replaced by numbers you have
evaluated the expression.
--The answer that results is called the
value of the expression.

13. x5 (2)5 2·2·2·2·2 32 Evaluate the expression x5 when x = 2.
First, show the substitution by using parentheses, then evaluate.
Directly to the left of
the exponent is x, not –x.
What is the base of the power? x5
(2)5
2·2·2·2·2 32
The base is x.

14. What is the base of the power?
Evaluate (3x)2 when x = 4.
What is the base of the power? 3x
Directly to the left of the exponent is the right parentheses, so everything within the parentheses is the base of the power.

15. To evaluate an expression involving more than one operation, mathematicians have agreed upon a certain order to prioritize the operations.
First: do operations that occur within
grouping symbols ( ) [ ] { }
Second: evaluate powers
Third: do multiplications and divisions
from LEFT to RIGHT
Fourth: do additions and subtractions from
LEFT to RIGHT

16. Grouping symbols like parentheses ( ), brackets { }, and braces [ ] are used to clarify or change the order of operations.
These symbols indicate that the expression inside the grouping symbol should be evaluated first.
A fraction bar can also be used as a grouping symbol. A fraction bar indicates that the numerator and the denominator should each be treated as a single value.

17. When simplifying within a grouping symbol, follow steps 2 – 4.
25 + [(1 + 3)2 – 7]
5(62 - 3•5) – 7
25 + [(4) 2 – 7)]
5(36 - 3•5) – 7
25 + (16 – 7)
5(36 – 15) – 7
25 + 9
5(21) – 7 34
105 – 7 98

18. 5