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1.2 – The Commutative & Identity Properties
Commutative Properties
Addition
For any numbers a and b, a  b  b  a . (We can change the order when
adding without affecting the sum.)
Multiplication
For and numbers a and b, ab  ba . (We can change the order when
multiplying without affecting the product.)
 Expressions such as 2  x and x  2 , which always result in the same
number when we substitute any value for their variables, are called
equivalent expressions.
Identity Properties
Addition
For any number a, a  0  a and 0  a  a . (Adding 0 to any number gives
that number.)
Multiplication
For any number a, 1  a  a and a 1  a . (Multiplying a number by 1 gives
that number.)
Dividing a Number by Itself
For any number a, a  0 ,
a
 1.
a
Example 1 – Write an equivalent expression for
Use
3
for 1.
3
6
by multiplying by 1.
7
Example 2 – Write an equivalent expression for
Use
a
for 1.
a
x
by multiplying by 1.
2
 When two or more numbers are multiplied to form a product, each
number is called a factor of the product. For example, 3  5  15 , so 3
and 5 are factors of 15.
 When the only common factor of the numerator and the denominator of a
fraction is 1, the fraction is in simplest form.
 The process of finding the simplest form is called simplifying.
Example 3 – Simplify.
a.
21
14
b.
L2 – pg 14 (11-29 odd)
40
60
c.
4ab
8a
d.
y
3 xy