General Information, Facts & Tables [Laws of Mathematics]

Overview

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The tables below outline the basic laws of mathematics.

Commutive, Associative and Distributive Laws

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Law

Example

 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

 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.