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Math 208 ALEKS
RED
Properties of real numbers
In this concept, you will be working with 10 properties of real numbers:
1. Commutative Property of Addition
2. Associative Property of Addition
3. Additive Identity Property
4. Additive Inverse Property
5. Distributive Property
6. Commutative Property of Multiplication
7. Associative Property of Multiplication
8. Multiplicative Identity Property
9. Multiplication Property of Zero
You will be given four or five true statements and asked to identify which of the 10
properties applies to this statement.
Keep the following chart handy:
PROPERTIES OF ADDITION
PROPERTIES OF MULTIPLICATION
Commutative
(order)
x + y = y + x
x • y = y • x
or
xy = yx
Associative
(grouping)
(x + y) + z = x + (y +
z)
(x • y) • z = x • (y • z)
or
(xy)z = x(yz)
Identity
(returns itself)
x + 0 = x
or
0 + x = x
x • 1 = x
or
1 • x = x
Inverse
(opposite
0 or 1)
x + (x) = 0
or
x + x = 0
=
=
1
•
1
1
•
1
x
x
x
x
or
Distributive
( • through + )
x(y + z) = xy + xz
or
(x + y)z = xz + yz
Multiplicative Property of
Zero
(multiply by 0 = 0)
0 • x = 0
or
x • 0 = 0
Now, let’s look at the chart and try to understand what it is telling us:
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 Spring '10
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