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General Information, Facts & Tables
[Laws of Mathematics]

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Overview

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The tables below outline the basic laws of mathematics.

See Also: Mathematical Constants, Mathematical Symbols
 

Commutive, Associative and Distributive Laws

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Law

Example

Commutive addition

a + b + c

=

c + b + a

=

b + c + a

Non commutive subtraction

a - b - c

¹

c - b - a

¹

b - c - a

Commutive multiplication

a * b * c

=

c * b * a

=

b * c * a

Non commutive division

a / b / c

¹

c / b / a

¹

b / c / a

Associative addition

a + b + c

=

(a + b) + c

=

a + (b + c)

Non associative subtraction

a - (b - c)

¹

(a - b) - c

 

 

Associative multiplication

a * b * c

=

(a * b) * c

=

a * (b * c)

Non associative division

a / (b / c)

¹

(a / b) / c

 

 

Distributive multiplication

a(b + c)

=

(a * b) + (a * c)

 

 

Distributive division

(b + c)/a

=

(b / a) + (c / a)

 

 

 

Transposition of Terms

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a = b / c \ b = a * c \ c = b / a

a / b = c / d \ a = bc / d \ b = ad / c \ c = ad / b \ d = bc / a

a + b = c \ a = c - b \ a + b - c = 0

a2 = b2 + c2 \ a = Ö(b2 + c2) \ b = Ö(a2 - c2) \ c = Ö(a2 - b2)

a = 1 / (dÖbc) \ a2 = 1 / (d2bc) \ b = 1/ (d2a2c) \ c = 1 / (d2a2b) \ d = 1 / (aÖbc)

 

Laws of Exponents

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Operation

Law

Multiplication

ax * ay = ax+y

Division

ax / ay = ax-y

Power

(ax)y = ax*y

Reciprocal

a-x = 1/ax

Fractional

ax/y = yÖax

Root

xÖ(a/b) = (xÖa) / (xÖb)

Product

xÖab = xÖa * xÖb

 

Dividing Fractions

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A fraction can be divided by inverting the second fraction and multiplying.
(a / b) / (c / d) = (a / b) * (d / c)
 

Notes

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The "Symbol" font is required to display the radical "Ö" symbol.