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Lesson
Exercises
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Rule
Identity Property of Multiplication
Any number
multiplied
by
1
is equal to the
number
itself.
a
⋅
1
=
a
Because of this, the number
1
is called the
Multiplicative Identity
.
Proof
Informal Justification
Consider a number
a
.
By the definition of multiplication,
a
multiplied by another number
n
can be written as
n
times the
addition
of
a
.
a
⋅
n
=
n
times
a
+
a
+
…
+
a
If
n
=
1
,
the sum has only one
term
.
a
⋅
1
=
1
time
a
Therefore,
a
⋅
1
is equal to
a
.
Also, by the
Commutative Property of Multiplication
,
1
⋅
a
=
a
.
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