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# Real Numbers Algebra

## The commutative and associative law for addition and more.

Commutative Law for Addition can be expressed as

a + b = b + a         (1)

Associative Law for Addition can be expressed as

(a + b) + c = a + (b + c)         (2)

Identity Law for Addition can be expressed as

a + 0 = 0 + a         (3)

Inverse Law of Addition can be expressed as

a + (-a) = (-a) + a = 0         (4)

### Associative Law for Multiplication

Associative Law for Multiplication can be expressed as

a · (b · c) = (a · b) · c         (5)

### Inverse Law for Multiplication

Inverse Law for Multiplication can be expressed as

a · (1 / a) = (1 / a) · a = 1, a ≠ 0           (6)

### Identity Law for Multiplication

Identity Law for Multiplication can be expressed as

(a) · (1) = (1) · (a)           (7)

### Commutative Law for Multiplication

Commutative Law for Multiplication can be expressed as

a · b = b · a         (8)

### Distributive Law

Distributive Law can be expressed as

a · (b + c) = a · b + a ·c         (9)

## Related Topics

• ### Basics

The SI-system, unit converters, physical constants, drawing scales and more.

## Related Documents

• ### Discrete Data Sets and their Mean, Median and Mode Values

Calculate the arithmetic mean, median and modal values from discrete data sets.
• ### Numbers - Square, Cube, Square Root and Cubic Root Calculator

Calculate square, cube, square root and cubic root. Values tabulated for numbers ranging 1 to 100.
• ### Roman Numerals

Roman numerals are a combinations of seven letters.

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## Citation

• The Engineering ToolBox (2008). Real Numbers Algebra. [online] Available at: https://www.engineeringtoolbox.com/real-numbers-algebra-d_1244.html [Accessed Day Month Year].

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10.2.10