July 22, 2024
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R2 – Division – Flipping

Flipping in R2 division can be applied to the individual Opposite Values or to the result to reverse their signs.

R2 Division Table

/1^1vi^iv
1^1^1vivi^
1v1v1^i^iv
i^i^iv1^1v
ivivi^1v1^

Flipping Opposite Values in R2

  • 6v/3iv = 6^/3iv = 2i^
  • 6v/3iv = 6v/3i^ = 2i^                       
  • 1^*(i^/1^) = 1^*(iv/1v)   = 1^*i = i^ 
    • Note that 2 flips cancel out i^/1^ = i^, iv/1v = i^

  • 1v*(1^/i^)  = 1v*(1v/iv)   1v*iv  = i^
  • 3^*(4i^/3v)  = 3^*(4iv/3v) = 3^*(4i^/3)  = 4i^
  • (3^*4i^)/3v = (3^*4iv)/3v =12iv/3v = 4i^
    • Note that multiplication part of the equation is associative

  • 3^*(4iv/3) = 3^*(4iv/3) =  (3^*4iv)/3 =  12iv/3 =   4iv
  • 3i^*(4v/3i^)= 3i^*(4^/3iv)= 3i^*(4i^/3)= 12v/3= 4v       
    • Note that the flip on the divisor cancels out the flip on the numerator. i.e. 4v/3i^ = 4i^/3 = 4^/3iv

Flipping Counters in R2

The flip sign applies to the result when used with a Counter. This is because Counters do not have an Opposite Sign to flip. For example:

  • 6iv/3 = 2i^

The flip on the Counter divisor cancels out the flip on the Opposite Value numerator. For example:

  • 3^*(4iv/3) = 3^*(4i^/3) = 3^*(4iv/3) = 12iv/3 = 4iv

Flipping Terms

The Opposite Value of a term must be worked out before the flipping can take place. An exception to this is where 2 flips happen together and cancel each other out. For example:

  • b*(a/b) = a
  • 2*2a = 4a

Conclusion

Try these examples of flipping and R2 division with our online calculator.

Next: Advanced Division

Previous: Definition of Division

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