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

Additive Identity Property

a + 0 = a

Sample

4 + 0 = 4

Multiplicative Identity Property

a • 1 = a

Sample

4 • 1 = 4

Additive Inverse Property

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.

Re: Properties of Real Numbers

Is there a question in all of that?

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.

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.

Re: Properties of Real Numbers

Quote:

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.