Transcript 1.1 PPT

Variables in Algebra
Variables in Algebra
Variable – A symbol, usually a letter of the alphabet, such
as the letter x, that is used to represent a number.
Variable expression– An expression, such as n – 5, that
consists of one or more numbers and variables along with one
or more arithmetic operations.
(Note: NOOOOO equal sign)
Numerical Expression– An expression that represents a
particular number.
Variables in Algebra

Evaluate a Variable Expression – write the expression,
substitute a number for each variable, and simplify the
result.
How Do You Describe a
Variable Expression?
Variable
Expression
5x, 5 · x, (5) (x), 5(x)
x
5
,x 5
x 5
x 5
Meaning
5 times x
Operation
Multiplication
x divided by 5
Division
x plus 5
Addition
x minus 5
Subtraction
State the meaning of the
variable expression and name
the operation
1.
2.
3.
4.
8 x
2w
7
n
6p
A
A
A
A
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Answer:
State the meaning of the variable expression
and name the operation
1.
2.
3.
4.
8
2
7
6
minus x; Subtraction
times w; Multiplication
divided by n; Division
plus p; Addition
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Evaluate a Variable Expression – write
the expression, substitute a number for
each variable, and simplify the result.
 Value of a Variable – A number that
may be substituted or assigned to a
particular variable; such as n = 3; or
x = 5.

Example 1: Evaluate each expression when n = 4
a.
n3
4+3
Substitute 4 for n. Simplify
7
b.
n 3
4-3
1
Substitute 4 for n. Simplify
Example 2: Evaluate each expression when x = 8
Substitute 8 for x. Simplify
a. 5x
5(8)
40
b.
x 4
8¸ 4
2
Note: No operation sign
between a variable and
number– indicates
multiplication problem.
Substitute 8 for x. Simplify
Example 3: Evaluate each expression when x = 4, y = 6,
z = 24.
a.
Recall: No
operation sign
between
variable(s) and a
number–
indicates
multiplication
problem.
5xy
Substitute 4 for x; 6 for y. simplify
5xy = (5)(4)(6)
= (20)(6)
 120
b.
zy
24 ¸ 6
4
Evaluate each expression when a = 6, b = 12, and c = 3
1.
4ac
A
2.
3.
a c
a bc
A
4.
ba
A
5.
bc
A
6.
c b
A
A
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Evaluate each expression when a = 6, b = 12, and c = 3
1.
4ac
Notice that all the numbers and letters are
together and that there are no operation
symbols which indicates that this is a
multiplication problem.
4ac  (4)(6)(3)
 ( 24)(3)
 72
Substitute the value for a = 6 and c = 3
into the problem and multiply
multiply
Simplified
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Evaluate each expression when a = 6, b = 12, and c = 3
a c
2.
Division Problem
a c  6 3
Another way to
solve division
problems is to
write them as
fractions and
simplify.
2
Substitute the value for a = 6 and c = 3
into the problem and divide
Simplified
a 6
a c    2
c 3
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Evaluate each expression when a = 6, b = 12, and c = 3
3.
a bc
Addition problem
a  b  c  6  12  3
 18 3
 21
Substitute the value for a = 6, b=12,
and c = 3 into the problem, then add
Add
Simplified
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Evaluate each expression when a = 6, b = 12, and c = 3
4.
ba
multiplication problem
ba  (12)(6)
 72
Substitute the value for b=12 and a = 6
into the problem, then multiply
Simplified
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Evaluate each expression when a = 6, b = 12, and c = 3
5.
bc
Subtraction problem
b  c  12  3
9
Substitute the value for b=12 and a = 3
into the problem, then Subtract
Simplified
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Evaluate each expression when a = 6, b = 12, and c = 3
6.
Divide both
numerator and
denominator by
the GCF = (3) to
reduce this
fraction.
c b
Division problem
c b  312
3

12
3 3
1


12  3
4
Substitute the value for c=3 and b = 12 into
the problem, then Divide
Note: It is better to rewrite this division
problem as a fraction.
This fraction can now be reduced to its
simplest form.
Simplified
It is OK to have a fraction
as an answer.
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