The document defines several key properties of real numbers: 1) The commutative properties state that addition and multiplication are unaffected by the order of numbers. 2) The associative properties state that grouping does not affect the sum or product of numbers. 3) The distributive property relates multiplication of a number and a sum to the individual products.

1. Real Number Properties
Students will identify real number
properties.

2. Definitions
• Commutative Property over Addition
says that we can add
numbers in any order
a+b=b+a

3. Definitions
• Commutative Property over
Multiplication
says that we can multiply
in any order
(a)(b) = (b)(a)

4. Definitions
• Associative Property over Addition
tells us that we can group
numbers in a sum any way
we want and get the same
answer.
(a + b) + c = a + (b + c)

5. Definitions
• Associative Property over
Multiplication
tells us that we can group
numbers in a product any way we
want and get the same answer.
(ab)(c)= (a)(bc)

6. Definitions
• Distributive Property
states that the product of a
number and a sum is equal to
the sum of the individual
products of addends and the
number.
a(b + c) = ab + ac

7. Definitions
• Identity Property for Addition
states that zero can be added to
any real number and the result is
that number.
a+0=a

8. Definitions
• Identity Property for Multiplication
states that one can be multiplied
by any real number and the result
is that number.
a .1 = a

9. Definitions
• Opposites or Additive Inverses
have a sum of 0.
a + (-a) = 0

10. Definitions
• Reciprocals or Multiplicative
Inverses
have a product of 1.
a . 1/a= 1

11. Definitions
• Absolute Value
the distance a number is from
zero on the number line.
I –a I = a
- I -a I = -a

12. In your composition notebook,
choose one of the following:
• How do you distinguish the
differences between the
commutative property over addition
and the associative property over
multiplication? Give one example of
each using variables and
constants.