Proposition: Distributivity Law For Rational Numbers

For arbitrary rational numbers \(x,y,z\in\mathbb Q\) with the binary operations addition "\( + \)" and multiplication "\(\cdot\)", the following distributivity laws hold:

\[\begin{array}{ccl} x\cdot(y+z)&=&(x\cdot y)+(x\cdot z).\quad\quad\text{"left-distributivity property"}\\ (y+z)\cdot x&=&(y\cdot x)+(z\cdot x)\quad\quad\text{"right-distributivity property"},\\ \end{array}\]

Proofs: 1

Proofs: 1 2 3 4


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References

Bibliography

  1. Kramer Jürg, von Pippich, Anna-Maria: "Von den natürlichen Zahlen zu den Quaternionen", Springer-Spektrum, 2013