Transcript algebraic expression - StCeciliaHonorsMath

Algebraic
Expressions
Honors Math – Grade 8
Get ready for the Lesson
Alana works at a beach arcade during summer vacation. Her salary
is $7.25 an hours plus a one-time bonus of $75. What algebraic
expression represents how much Alana will earn over the summer?
An algebraic expression is a mathematical expression consisting
of numbers, variables and operations..
A variable is a symbol, usually a letter,
representing one or more numbers.
To write an algebraic expression
1. Define a variable for the unknown.
2. Write an expression in terms of the
same variable for any other
unknown quantities.
7.25h  75
A term of an algebraic expression is a number, a variable or a
product or quotient of numbers and variables.
The numerical part of a term that contains variables is the
numerical coefficient.
The variable, or variables, of a term is called the literal coefficient.
A term that does not have variables is called a constant.
Numerical coefficient
Literal coefficient
Name the coefficient.
xy
19 x  y   11
8
19 x 19
y
1
xy
8
1
8
4 terms
To write an algebraic expression, you must be able to determine the mathematical
operation(s) associated with word phrases.
Addition
a+b
a plus b
The sum of a and b
a and b are added
a is increased by b
b is added to a
b more than a
the number that exceeds a by b
Subtraction
a–b
a minus b
The difference between a and b
b subtracted from a
a decreased by b
a diminished by b
b less than a
a reduced by b
Multiplication
a b, a x b, (a)(b), a(b)
a times b
the product of a and b
b multiplied by a
Division
a divided by b
The quotient of a and b
a b
a
b
Write an algebraic expression for each verbal
expression.
Verbal Expression
Key Words
The number of minutes,
m, increased by 10
Increased bysuggests addition.
The variable is already defined.
28 subtracted from y
Subtracted from suggests
subtraction.
The variable is already defined.
Twice the number
of apples, a
Twice implies multiplication.
The variable is already defined.
The number of girls,
g, divided by 5
Divided by suggests division.
The variable is already defined.
Algebraic Expression
m  10
y  28
2a
g 5
g
5
Algebraic expressions may contain more than one operation and
may involve the use of grouping symbols. Let’s take a closer look!
Write an algebraic expression for each verbal
expression.
Verbal Expression
38 diminished by the
absolute value of the
product of 7 and number
Key Words
Diminished by suggests subtraction
Product suggests multiplication
Define a variable.
11 more than one
fourth of a number.
More than suggests subtraction.
Of suggest multiplication
Define a variable.
10 times the difference
of 15 and a number
Times implies multiplication.
Difference suggests subtraction
2 times the quantity 8
plus n squared.
The sum of the
opposite of a number
and 12 divided by 9
Define a variable.
Times suggests division.
Squared suggests an exponent.
The variable is already defined.
Sum suggests addition.
Opposite of a number
Divided by suggests division
Define a variable.
Algebraic Expression
38  7n
1
x  11
4
10(15  h)
2(8  n )
2
 m  12
9
Write an algebraic expression for each verbal
expression.
The value in cents of d dimes and n nickels.
The value of 1 dime is 10 cents, so the value of d dimes is 10d cents.
The value of 1 nickel is 5 cents, so the value of n nickels is 5n cents.
The word total indicates addition, so the total value in cents is…
10d  5n
Not all word phrases translate directly into algebraic expressions.
Sometimes you need to interpret a situation and apply a familiar fact.
To evaluate an algebraic expression, you substitute numbers for the
variables in the expression and then compute using the Order of
Operations.
KEY CONCEPT
The Substitution Principle
For any numbers a and b, if a = b, then a may be replaced
with b.
THINK…
PLUG IT IN!
PLUG IT IN!
Evaluate the following expressions when
d = 5000
Substitute 5000 for d.
Then simplify using
the Order of
Operations.
d
d
50
4d  2500
Evaluate the following expressions when
t=40, u=120, v=100, and w=75
Substitute:
100 for v
75 for w
2
v
 3w
40
Simplify using
the order of
operations.
Substitute:
100 for v
75 for w
50 for t
3v
2t 
w