An Introduction to Algebra and Simplifying Algebraic Expressions
An Introduction to Algebra and Simplifying Algebraic
Expressions
Objective: To use the order of
operations and distributive
property to simplify expressions. |
Introduction
In arithmetic , we
perform mathematical
operations with specific numbers. In
algebra, we perform these same basic
operations with numbers and variables,
which are letters that stand for
unknown quantities . |
Definitions
variable – a symbol, usually a letter, that
represents one or more numbers
algebraic expression – a math phrase with
numbers, variables, and operation symbols
evaluate – substitute and simplify |
The following are some basic mathematical
properties that we will apply:
Commutative: a + b = b + a; ab = ba
Associative: (a + b) + c = a + (b + c);
(ab)c =a(bc)
Distributive: a(b + c) = ab +ac
a + 0 = a
a(0) = 0
a + (-a) = 0
a(1) = a |
Order of Operations, pg. 202
1. Grouping symbols (parentheses,
brackets , fraction bar)
2. Exponents
3. Multiply and divide in order from left
to right.
4. Add and subtract in order from left to
right. |
P.E.M.D.A.S.
Please Excuse My Dear Aunt Sally!
1. P – parentheses (any grouping symbols)
2. E – exponents
3. M/D – multiply/divide (left to right)
4. A/S – add/subtract (left to right) |
Simplify using the Order of
Operations.
|
Your Turn: Simplify using the
Order of Operations.
|
Evaluating an Expression
To evaluate 2x - y when x = 5 and y = -3,
replace the variables with their values in
parentheses and simplify.
|
Evaluate if x = 2.
|
Simplifying Algebraic Expressions
term – a number, a variable, or a
product of a number & variable(s)
constant – a number that does not
change in value
coefficient – a numerical factor of a
term (the number in front of a variable)
like terms – exactly the same variable
and power |
An explanation
Terms are always separated by a plus
(or minus) sign. For example, the
expression 2x - 3y has two terms , 2x
and -3y. In this expression, 2 and -3
are constants, x and y are variables
with 2 being the coefficient of x and -3
the coefficient of y.
The expression 2x +3y -5 has 3 terms. |
Example: Simplify each expression by
combining like terms .
|
Distributive Property
If an algebraic expression that appears
in parentheses cannot be simplified,
then multiply each term inside the
parentheses by the factor preceding the
parentheses . Then combine like terms. |
Distributive Property Practice
|
Parentheses If an
expression inside parentheses is
preceded by a “+” sign, then remove
the parentheses by simply dropping
them. For example:
3x + (4y + z) = 3x + 4y + z. |
Parentheses If an
expression in parentheses is
preceded by a “-” sign then it is removed
by changing the sign of each term inside
the parentheses and dropping the
parentheses. For example,
3x – (4y – z) = 3x – 4y + z.
(This is like distributing a negative one .) |
Simplify
|
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