R2 – Multiplication – Simple

This post looks at some simple multiplication of Opposite Values together and using counters. The examples show the commutativity, associativity and distributivity of R2 math multiplication.

R2 Unitary Multiplication Table

Simple Multiplication with R2 Opposite Values

• 3i^v*4^{^} = 12i^v
• 4^{^}*3i^v = 12i^v    
• 4i^v*3i^v = 12^v
• 3i^v*4i^v = 12^v
• 3i^v*4i^{^} = 12^{^}
• 4i^{^}*3i^v = 12^{^}         
  • Note that this shows that multiplication is commutative

• (2i^v*4i^{^})*3^v = 8^{^}*3^v = 24^v
• 2i^v*(4i^{^}*3^v ) = 2i^v*12i^v = 24^v
• (4i^v*3^v)*2^{^}  = 12i^{^}*2^{^} = 24i^{^}
• 4i^v*(3^v*2^{^})  = 4i^v*6^v =  24i^{^}
  • Note that this shows that multiplication is associative

• 5i^v(6^{^} + 3^v)  = 5i^v*3^{^}= 15i^v
  • = 5i^v*6^{^} + 5i^v*3^v = 30i^v + 15i^{^}= 15i^v
  • Note that this shows that multiplication is distributive

• 5i^v(6i^{^} + 3^v) = 5i^v*6i^{^} + 5i^v*3^v =  30^{^} + 15i^{^}                   
  • 6i^{^} + 3^v cannot be reduced any further and multiplier 5i^v must be distributed to resolve

• (5i^v + 2^{^})(6i^{^} + 3^v) = (5i^v*6i^{^} + 5i^v*3^v + 2^{^}*6i^{^} + 2^{^}*3^v)  
  • =  30^{^} + 15i^{^} + 12i^{^} + 6^v = 24^{^} + 27i^{^}           
• (6i^{^} + 3^v) (5i^v + 2^{^}) = (6i^{^}*5i^v + 6i^{^}*2^{^} + 3^v*5i^v + 3^v*2^{^})  
  • =  30^{^}  + 12i^{^}  + 15i^{^}  + 6^v = 24^{^}+ 27i^{^}
    • Note that this shows that multiplication is commutative

Multiplication with Counters

• 5(6^{^} + 3^v) = 15^{^} = 5(6^{^}) + 5(3^v) = 30^{^} + 15^v = 15^{^}

A flip sign in front of a Counter means that the Opposite Sign should be changed to the other Opposite Sign after multiplication.

• ^–5(6^{^} + 3^v) = ^–5(3^{^}) = 15^v
  • = ^–5(6^{^}) + ^–5(3^v) = 30^v + 15^{^} = 15^v
• ^–2*^–2*2i^{^} = 8i^{^}
  • Note that two flips cancel each other out

Counters cannot be multiplied by themselves, because the result of any calculation must be an Opposite Value. So 3*5*2i^{^} = 30i^{^} is valid, however, 3*5 = 15 is not permitted as 15 is not a valid result as it is not an Opposite Value.

Conclusion

Try all these examples of multiplication with our online calculator.

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