Download The Commutative, Associative, and Distributive Laws

The Commutative,
Associative, and
Distributive Laws
Recall: Algebra is the study of
how to rewrite mathematical
expressions without changing
their value.
Two different expressions that
have the exact same value are
said to be equivalent.
Goal:
Examine and apply three
laws of algebra
The Commutative Law
For addition:
If a and b are variables that stand
for any number, then
a+b=b+a
Translate into English:
Examples:
The Commutative Law
The Associative Law
For multiplication:
For addition:
If a and b are variables that stand
for any number, then
If a, b and c are variables that
stand for any number, then
ab=ba
a + (b + c) = (a + b) + c
Translate into English:
Translate into English:
Examples:
Examples:
1
The Associative Law
For multiplication:
If a, b and c are variables that
stand for any number, then
Examples: Use both the
commutative and associative laws to
find equivalent expressions:
1. (x + 3) + 9
a . (b . c) = (a . b) . c
Translate into English:
2. 3(t . 4)
Examples:
The Distributive Law
If a, b and c are variables that
stand for any number, then
a(b + c) = ab + ac
Another name: the Distributive
Law of Multiplication over
Addition.
In an algebraic expression, terms
are the numbers, variables, or
expressions that are added.
Examples: List the terms.
y
s+y
3x + + 5
2
Examples:
In an algebraic expression, factors
are numbers, variables, or
expressions that are multiplied.
Examples: List the factors.
xyz
2(7 + y)
The process of factoring finds an
equivalent expression of factors.
Example: We know that
2(7 + y)
can be written as
14 + 2y
using the distributive law. So the
factors of 14 + 2y are 2 and (7 + y).
2
Factoring “undoes” multiplication.
Examples: Factor.
1. 3y + 9
2. 5 + 15t + 10
3. xy + y
3