10 Easy Algebra Step-by-Step
- Associative Property of Multiplication. (ab)c = a(bc). This property says
that when you have three numbers to multiply together, the fi nal product
will be the same regardless of the way
you group the numbers (two at a time)
to perform the multiplication.
Example
Suppose you want to compute
72
1
2
2 ⋅. In the order given, you have
two ways to group the numbers for
multiplication:
1
214
1
2
77
1
2
()^72 ⋅=⋅=o ⋅()^2 =^771 =^71
2
2 ⋅
Either way, 7 is the fi nal product.- Additive Identity Property. There exists a real number 0, called the additive
identity, such that a + 0 = a and 0 + a = a. This property guarantees that you
have a real number, namely, 0, for which its sum with any real number is the
number itself.
Examples
− 80 + == 08 +− − 8
5
6
00
5
6
5
6
+=+ 00 =
- Multiplicative Identity Property. There exists a real number 1, called the
multiplicative identity, such that a · 1 = a and 1 · a = a. This property
guarantees that you have a real number, namely, 1, for which its product
with any real number is the number itself.
Examples
511 = 155 = 5
−⋅ ⋅−=−7
8
11 =
7
8
7
8
- Additive Inverse Property.For every real number a, there is a real
number called its additive inverse, denoted −a, such that a + −a = 0
and −a + a = 0. This property guarantees that every real number has an
additive inverse (its opposite) that is a real number whose sum with the
number is 0.
The associative property is needed when
you have to add or multiply more than two
numbers because you can do addition or
multiplication on only two numbers at a
time. Thus, when you have three numbers,
you must decide which two numbers you
want to start with—the fi rst two or the last
two (assuming you keep the same order).
Either way, your fi nal answer is the same.