# Thread: Properties of Real Numbers

1. ## Properties of Real Numbers

This is a reference chart for anyone who needs to review algebra 1 real number properties or use in class.

Property (a, b and c are real numbers, variables or algebraic expressions)

Distributive Property
a • (b + c) = a • b + a • c
Sample
3 • (4 + 5) = 3 • 4 + 3 • 5

Commutative Property of Addition
a + b = b + a
Sample
3 + 4 = 4 + 3

Commutative Property of Multiplication
a • b = b • a
Sample
3 • 4 = 4 • 3

Associative Property of Addition
a + (b + c) = (a + b) + c
Sample
3 + (4 + 5) = (3 + 4) + 5

Associative Property of Multiplication
a • (b • c) = (a • b) • c
Sample
3 • (4 • 5) = (3 • 4) • 5

a + 0 = a
Sample
4 + 0 = 4

Multiplicative Identity Property
a • 1 = a
Sample
4 • 1 = 4

a + (-a) = 0
Sample
4 + (-4) = 0

Multiplicative Inverse Property
a(1/a), where a cannot be zero.
Sample
2(1/2) = 1

Zero Property of Multiplication
a • 0 = 0
Sample
4 • 0 = 0

Closure Property of Addition
a + b is a real number
Sample
10 + 5 = 15 (a real number)

Closure Property of Multiplication
a • b is a real number
Sample
10 • 5 = 50 (a real number)

Addition Property of Equality
If a = b, then a + c = b + c.
Sample
If x = 10,
then x + 3 = 10 + 3

Subtraction Property of Equality
If a = b, then a - c = b - c.
Sample
If x = 10,
then x - 3 = 10 - 3

Multiplication Property of Equality
If a = b, then a • c = b • c.
Sample
If x = 10,
then x • 3 = 10 • 3

Division Property of Equality
If a = b, then a / c = b / c,
assuming c ≠ 0.
Sample
If x = 10,
then x / 3 = 10 / 3

Substitution Property
If a = b, then a may be substituted for b, or conversely.
Sample
If x = 5, and x + y = z,
then 5 + y = z.

Reflexive (or Identity) Property of Equality
a = a
Sample
12 = 12

Symmetric Property of Equality
If a = b, then b = a.
Sample
If 3 = 3*1, then 3*1 = 3

Transitive Property of Equality
If a = b and b = c,
then a = c.
Sample
If 2a = 10 and 10 = 4b,
then 2a = 4b.

Law of Trichotomy
Exactly ONE of the following holds:
a < b, a = b, a > b
Sample
If 8 > 6, then 8 6 and
8 is not < 6.

2. ## Re: Properties of Real Numbers

Is there a question in all of that?

3. ## Re: Properties of Real Numbers

Plato,

This is a reference chart for anyone who needs to review algebra 1 real number properties or use in class.

4. ## Re: Properties of Real Numbers

Those "properties" are all true of the rational numbers as well as the real numbers. To specifically talk about the real numbers you have to add a "completeness property": if a set of real numbers has an upper bound then it has a least upper bound.

5. ## Re: Properties of Real Numbers

Originally Posted by HallsofIvy
Those "properties" are all true of the rational numbers as well as the real numbers. To specifically talk about the real numbers you have to add a "completeness property": if a set of real numbers has an upper bound then it has a least upper bound.
This is a reference chart for anyone who wants or needs to quickly review algebra 1 properties. It is not my intention to tutor or teach properties of real numbers.

6. ## Re: Properties of Real Numbers

Hi,
I have anice video about these properties but on rational numbers. But no worries, it works with real numbers also. Check it out.