Transcript 1-1 Variables and Expressions

Pre Test
Translate each word into a mathematical operation.
1)
2)
3)
4)
5)
increase
decrease
more than
less than
product
+
−
+
−
•
6)
7)
8)
9)
10)
plus
difference
quotient
sum
times
+
−
÷
+
•
Write and answer the following problems.
11) Simplify. −42
12) Write 2y • 2y • 2y in exponential form.
1-1 Variables and
Expressions
You would be
wise to
listen
carefully and
take notes!
Algebra 1
Be smart correct your
odd homework
problems after
you complete
them!
Glencoe McGraw-Hill
Linda Stamper
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
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.
xy
xy 
 x y
x y 
xy
Use good form in an answer!
In each expression, the quantities being multiplied are
called factors, and the result is called the product.
An expression like 43 is called a power.
base 
43  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.
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
Phrase
6 + n
Sentence The difference of a number
and three is five.
n – 3 = 5
Sentence Seven times a number
is less than 50.
7n < 50
When choosing a variable for an unknown, it may be helpful
to select a Sentences
letter that must
relates to the unknown value (for
example: let have
a represent
a verb!age). If a variable is given use it!
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.
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 nnumber
–
d. 10 less the product of 5 and a number cubed
10 – 5n3
e. The quotient of a number and six.
n
Use a fraction
6
bar to designate
division!
Example 1 Write the phrase as an algebraic expression.
a. 11 greater than a number
Did you use a
n + 11
fraction bar
b. a number subtracted from 15
to designate
division?
15 – n
c. The sum of a number and 30
n + 30
d. Maria’s age minus 27
a – 27
18
e. The quotient of 18 and a number
n
f. The sum of a number and ten, divided by two.
n  10
2
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
3
n
c. n cubed divided by 2
2
b
d. 9 more than the quotient of b and 5  9
5
1
a
e. one third the original area of a a or
3
3
f. thirteen less than a number
n - 13
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 8
Example 6
Example 7
2
2
(-3)
-3
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.
Pre Test
Write and answer the following problems in your
spiral notebook.
1) Simplify. −42 −16
3
2) Write 2y • 2y • 2y in exponential form. (2y)
−4•4
A power applies only
to what is directly
in front of it.
The 2y must be
in parentheses!
1-A2 Pages 8–9, #13–29,46–54.