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Field Axioms: Closure Commutativity Associativity Distributivity …

- - - - \( \frac{a\cdot d}{b\cdot d} = \frac{a}{b} \)
        
        \( \frac{a}{b}+\frac{c}{d} = \frac{a\cdot d+b\cdot c}{b\cdot d} \)
      - \( ~ \)
      - \( ~ \)
        
        \( \frac{\left(\frac ac\right)}{\left(\frac bd\right)} = \frac{ad}{bc} \)
    - - \( ~ \)
        
        \( \left(\frac{b}{d} \right)^{-1}=\frac {d}{b} \)