1-1 Variables and Expressions

1
1-1 Variables and Expressions
You would be wise to listen carefully and take
notes! Copy material that is highlighted the same
color as the above title.
In this section we are going to learn about
mathematical expressions and how to translate
verbal expressions into mathematical expressions.
Algebra 1A by Gregory Hauca Glencoe
adapted from presentations by
Linda Stamper
2
Pre Quiz
Write and translate each word into an operation
symbol.
6)
1) increase
6) plus

1)

2)
7)
2) decrease
7) difference
-
-
3)
8)
3) more than
8) quotient


4)
9)
4) less than
9) sum
-

5)
10)
5) product
x
10) times
x
Write and answer the following problems.
3
In Algebra, an expression is a mathematical
phrase that contains operations, numbers, and/or
variables..
You can use letters to represent one or more
numbers. When a letter is used to represent a
value that can change or vary, it is called a
variable.
An expression that represents a particular number
is called a numerical expression.
Ex. 3 6 3
A variable expression consists of numbers,
variables and operations.
Ex. 3x2 2x - 1
numbers- ex. 2,-3, p
variables letters ex. a,x,y
operations - addition, subtraction,
multiplication and division , -, ,
4
Multiplication Symbols
In variable 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.
Example. the product of x and y
In general, good algebraic form is the xy version!
Examples. 2y, 3xy
In each expression, the quantities being
multiplied are called factors, and the result is
called the product.
5
Powers.
Powers consist of a base and an exponent
Example
exponent
43
base
word description four to the third power or
four cubed
factored form 4 4 4
A power is a short way of writing a repeating
multiplication.
evaluated form 64
6
Ex.1 Express the power 72 in words. Then write
the factored form and evaluate it.
Ex.1
1. Write problem.
72
2. Write word description.
seven to the second power
or seven squared
7 7
3. Write factored form.
4. Evaluate.
49
7
Writing expressions in exponential or power form.
Ex.2
Ex.3
Ex.4
y y y y
5 5 5
3x 3x 3x 3x
y4
53
(3x)4
Must have parentheses!
Evaluating expressions.
Ex.7
Ex.5
Ex.6
-32
(-3)2
2 2 2 2
5 5 5
-(3 3)
-3 -3
16
125
-9
9
Remember! An exponent applies only to what is
directly in front of it.
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In English there is a difference between a phrase
and a sentence. Sentences have verbs and phrases
do not.
Phrases are translated into expressions.
Sentences are translated into equations and
inequalities.
Remember! A numeric expression is made up of
numbers and operations (ex. 5 3). A variable
expression is made up of variables, numbers and
operations. (ex. 3 2x).
In this section we are only going to translate
phrases into expressions.
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Words representing operations.
add
subtract
multiply
divide
plus
minus
times
quotient
sum
difference
product
of
increased by
decreased by
total
diminished by
twice
less
more than
less than
added to
subtracted from
10
Translating phrases into variable expressions.
1. The sum of a number and 30
n 30
2. 11 greater than a number
n 11
Note that translation of this phrase switches
the order of what is read. The expression 11 n
would NOT be correct.
3. A number decreased by 75
n 75
4. a number subtracted from 15
15 n
5. The product of 5 and a number
5n
The translation of this phrase also switches
the order of what is read.
6. The product of a number and 4
4n
Not 5n or 5(n) or (5)(n)
n 6
n 6
In products of numbers and variables the number
is always placed first. Do not write n4 .
7. The quotient of a number and 6
Use a fraction bar in algebra to designate
division! Not a symbol. The first number is
always the numerator (on top)
11
Multiple Operation Phrases
Some phrases require more than one operation or
variable when translating them. In some you will
need grouping symbols to show the correct order
of operations.
1. Twice a number plus 7
2n 7
2 n
7
2. 5 more than the product of a number and 4
4n 5
4 n
5
3. The difference of 8 and three times a number
8 3n
8 -
3 n
4. A number cubed divided by 2
2
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Class Practice
Translate
n - 12
a number minus 12
six times a number
6n
a number divided by 8
15 n
the sum of 15 and a number
n 6.7
the difference of a number and 6.7
the quotient of 17 and a number
13
Translate
n 15
15 more than a number
6n
the product of a number and 6
not n6
5.2 less than a number
the product of 6 and a number, subtract 10
6n
- 10
the quotient of a number and 10, plus 2
2
2
twice the sum of a number and 15
(n 15)
the difference of a number and 6, divided by 4
not 2n 15
14
Homework

• HW1A2 Pages 8-9
  13-22,26,28,30-33,46.

15
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16
Whiteboard Practice
Translate A number minus 12
n - 12
Translate six times a number
6n
Translate a number divided by
8
17
Translate the sum of 15 and a
number
15 n
Translate the difference of a
number and 6.7
n 6.7
Translate The quotient of 17
and a number
18
Translate 15 more than a
number
n 15
Translate the product of a
number and 6
6n
not n6
Translate 5.2 less than a
number
19
The product of 6 and a number, subtract 10
6n
- 10
The quotient of a number and 10, plus 2
2
20
Twice the sum of a number and 15
2
(n 15)
not 2n 15
The difference of a number and 6, divided by 4
21
Ex.1.
a. 11 greater than a number
n 11
b. a number subtracted from 15
15 n
Did you use a fraction bar to designate division?
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.
22
Writing word phrases as algebraic expressions.
a. The difference of a number and 7
n 7
b. 32 increased by a number
32 n
Use a fraction bar to designate division!
c. 25 less than a number
25
n

The number always comes before the variable?
d. The quotient of a number and six.
n 6
e. The product of a number and five
5n
f. 10 less the product of 5 and a number cubed
10 5n3
23
Ex.1
a. 11 greater than a number
n 11
b. a number subtracted from 15
15 n
Remember! Use a fraction bar to designate
division?
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.
24
Ex.2
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
n - 13
f. thirteen less than a number
25
Translating phrases into variable expressions.
Addition phrases
a. The sum of a number and 30
n 30
b. 12 plus a number
12 a
c. 32 increased by a number
32 x
d. 11 greater than a number
p 11
e. 7 more than a number
y 7
Note that translation of this phrase switches
the order of what is read. The expression 11 p
would NOT be correct.
The translation of this phrase also switches
the order of what is read. The word than often
indicates you may need to switch.
26
Subtraction phrases
a. The difference between a number and 7
n 7
b. A number minus 27
x 27
c. A number decreased by 75
a 75
d. 25 less than a number
y 25
e. a number subtracted from 15
15 p
Note that translation of this phrase switches
the order of what is read. The expression 25 - y
would NOT be correct.
The translation of this phrase also switches
the order of what is read.
27
Multiplication phrases
a. The product of 5 and a number
5n
Not 5n or 5(n) or (5)(n)
b. The product of a number and 5
5n
In products of numbers and variables the number
is always placed first. Do not write n5 .
c. Twice a number
2p
d. 300 times a number
300x
Twice means 2 times.
e. A number times 7
7a
Remember in products the number always comes
before the variable.
28
Division phrases
a. The quotient of a number and 6
n 6
n 6
Use a fraction bar in algebra to designate
division! Not a symbol. The first number is
always the numerator (on top)
b. The quotient of 18 and a number
18 x
c. A number divided by 12
a 12