1'1 Variables in Algebra

1
Pre TestTranslate each word into a mathematical
symbol.

1) increase
6) plus

-
2) decrease
7) difference
-

3) more than
8) quotient


4) less than
9) sum
-

5) product

10) times
Write and answer the following problems. 11)
Simplify. -42 12) Write 2y 2y 2y in
exponential form.
2
1-1 Variables and Expressions
You would be wise to listen carefully and take
notes!
Be smart -correct your odd homework problems
after you complete them!
Algebra 1 Glencoe McGraw-Hill
Malinda Young
3
In algebra, variables are symbols used to
represent unspecified numbers or values. Any
letter may be used as a variable.
An expression that represents a particular number
is called a numerical expression.
Example 3 2
An algebraic expression consists of one or more
constants and variables along with one or more
arithmetic operations.
constants - numbers
variables - letters
operations - addition, subtraction,
multiplication and division
Example of an algebraic expression 3x 2
4
In algebraic expressions, a raised dot or
parentheses are often used to indicate
multiplication as the symbol x can be easily
mistaken for the variable x. Here are some ways
to represent the product of x and y.
Use good form in an answer!
In each expression, the quantities being
multiplied are called factors, and the result is
called the product.
5
An expression like 43 is called a power.
43
base ?
? exponent
or power
word form four to the third power
four cubed
factor form 4 4 4
evaluated form 64
To evaluate an expression means to find its value.
The word power can also refer to the exponent.
6
Writing Algebraic Expressions
In English there is a difference between a phrase
and a sentence. Phrases are translated into
mathematical expressions. Sentences are
translated into equations or inequalities.
The sum of 6 and a number
6 n
Phrase
The difference of a number and three is five.

Sentence
n 3 5
Seven times a number is less than 50.
Sentence
7n lt 50
When choosing a variable for an unknown, it may
be helpful to select a letter that relates to the
unknown value (for example let a represent
age). If a variable is given use it!
Sentences must have a verb!
Sentences must have a verb!
7
The product of five and a number
5n
The product of a number and five
Would you say 5 notebooks or notebooks 5?
5n
Write your answer in good form - the number comes
before a variable in a term involving
multiplication.
8
Write an algebraic expression for each word
phrase.
a. The difference of a number and 7
n 7
b. 32 increased by a number
32 n
c. 25 less than a number
25
n

d. A number decreased by 75
n 75
e. The quotient of a number and six.
n 6
Use a fraction bar to designate division!
9
Example 1 Write the phrase as an algebraic
expression.
a. 11 greater than a number
Did you use a fraction bar to designate division?
n 11
b. a number subtracted from 15
15 n
c. The sum of a number and 30
n 30
d. Marias age minus 27
a 27
18 n
e. The quotient of 18 and a number
f. The sum of a number and ten, divided by two.
10
Example 2 Write the phrase as an algebraic
expression.
a. eight more than a number
n 8
b. seven less the product of 4 and a number x
7 4x
c. n cubed divided by 2
d. 9 more than the quotient of b and 5
e. one third the original area of a
f. thirteen less than a number
n - 13
11
Write in exponential form (as a power).
Example 3
Example 4
Example 5
y y y y
3x 3x 3x 3x
5 5 5
(3x)4
53
y4
Evaluate.
Example 7
Example 5
Example 6
-32
(-3)2
5 5 5
2 2 2 2
125
16
-9
9
Must have parentheses!
A power applies only to what is directly in front
of it.
12
Pre Test Write and answer the following problems
in your spiral notebook. 1) Simplify. -42 2)
Write 2y 2y 2y in exponential form.
-16
(2y)3
- 4 4 A power applies only to what is directly
in front of it.
The 2y must be in parentheses!
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Homework
1-A1 Page 8 13-29,49-54,