Section 1.3 Algebraic Expressions
Sheldon won some money in a biking completion. He has two choices on how he
gets paid.
Choice #1:
$20 per week for one year
Choice # 2:
$12 per week for one year plus $400 cash now
Questions
1.Which method would pay Sheldon more money?
Choice 1
choice 2
20x 52= 1040
12x 52 +400
624+400
1024
2.Using Choice #1, how much money would Sheldon have in
A)
4 weeks?
20 4 = 80
B)
10 weeks?
20x 10 = 200
3.Describe a rule you can use for Choice #1 to calculate the total money Sheldon
receives at any time during the year.
20 x the number of weeks
20x W
4.Using Choice #2, how much money would Sheldon have in
A)
12 weeks?
12 x 12 +400
144+400
544
B)
30 weeks? 12x30+400
360+400
760
5.Describe a rule you can use for Choice #2 to calculate the total money Sheldon
receives at any time during the year.
Multiply the number of weeks by 12 and add on 400........... so 12W + 400
Important Terms
Expression:
consists of numbers and/or variables which are related by +,-, ⨉, or
÷. It does NOT have an equal sign.
Variable:
a letter that represents a quantity that can change or vary
Numerical Coefficient: the number multiplied by a variable. If there is no
number in front of a variable the numerical coefficient is
automatically 1.
Constant Term: the number in an expression that does not change.... it stays
constant. It has no variable attached.
8n + 3
Numerical
Coefficient
Expression
4x + 7
Constant
Variable
Numerical Coefficient
4
Variable
X
Constant
7
3x + 2
3
X
2
7j -1
7
J
1
c+1
1
C
1
m
1
M
8
5 + 3g
8
3
G
5
1
y
-2
0
-2 + y
Writing Algebraic Expressions
Operation
Addition
Words
add
the sum of
more than
increased by
the total of
plus
Subtraction subtract from
difference
less ( less than)
decreased by
take away
reduced by
minus
Multiply
multiply
times
the product of
multiplied by
of
double
triple
Division
divide
divided by
the quotient of
the ratio of
equal amounts of
per
Examples
Five more than a number → n+5
The sum of a number and ten →n+10
A number increased by 4 →n+4
Seven plus a number →7+n
Five less than a number →n-5
A number decreased by six →n-6
A number reduced by eight →n-8
The number subtracted from twenty →20-n
The product of a number and four →4n
Five times a number →5n
A number doubled →2n
A number tripled →3n
A number divided by two →n/2
A number shared by ten people →n/10
The quotient of a number and three →n/3
Twelve is divided by a number →12/n
Write an algebraic expression that has...
A). A variable m, a numerical coefficient 4 and a constant term of 7. (4m+7)
B). A variable g, a numerical coefficient -3 and no constant term. (-3g)
C). A variable y, a numerical coefficient 1 and a constant term of -2. (y-2)
Evaluating an Algebraic Expression
To evaluate an algebraic expression means to substitute a number for the variable
and determine the value of the expression.
A). Evaluate
2m  5 if m = 3.
2(3) +5
2 x 3 +5
6+5
11
B). Evaluate
1
d  6 if d = 20.
2
½ (20)-6
20/2 -6
10-6
4
C). Evaluate
4  x if x = 1.
4-1
3
D). Evaluate 8 
m
if m = 6.
2
8 – 6/2
8-3
5
Complete Pages 18-19 #’s 1, 2, 4, 5, 7, 8