R1 – Division – Simple

This post covers simple math division using Opposite Values and Counters in R1.

Rotation Division Table.

The table shows the result of division by 1^{^} and 1^v.

/	1^	1v
1^	1^	1v
1v	1v	1^

Simple Division with R1 Opposite Values

• 1^{^}/0 – undefined
• 1^v/0  – undefined

As in classical numbers, you cannot divide by 0.

• 6^{^}/3^{^}  = 2^{^}
• 6^v/3^{^}  = 2^v
• 6^{^}/3^v  = 2^v and 3^v/6^{^}  = 1/2^v
  • This shows that division is not commutative.

• (24^{^}/8^v)/2^v = 3^v/2^v = 3/2^{^}
• 24^{^}/(8^v/2^v) = 24^{^}/4^{^} = 6^{^}
  • This shows that division is not associative.

• (11^{^} + 5^v)/(2^{^} + 5^v)  = 6^{^}/3^v = 2^v 

A flip sign in front of an Opposite Value means that the Opposite Sign should be changed to the other Opposite Sign before division

• 6^{^}/^–3^v  = 6^{^}/3^{^} = 2^{^}
• ^–6^{^}/^–3^v  = 6^v/3^{^} = 2^v = 6^{^}/3^v
  • Two flips cancel each other out

Simple Division with R1 Counters

• 6^v/3 = 2^v
• 6/3 = 2
  • Division of two counters can only happen when associated with a term or an Opposite Value.
• 6^{^}/^–3  = 2^v
  • Flipping by the Operator is possible in division. In other words, flipping by the Operator implies the result is flipped.
• ^–6^{^}/^–3  = 6^v/^–3 = 2^{^} = 6^{^}/3
  • Two flips cancel each other out

Conclusion

Try these examples of simple R1 division with our online calculator.

Next: Advanced

Previous: Definition