This post looks at some simple multiplication of Opposite Values together, using flip signs and with counters. The examples show the commutativity, associativity and distributivity of R1 math multiplication.
R1 Unitary Multiplication Table
| * | 1^ | 1v |
| 1^ | 1^ | 1v |
| 1v | 1v | 1^ |
Simple Multiplication with R1 Opposite Values
- 1^*0 = 0
- 1v*0 = 0
- 1^*1v = 1v
- 1^*1^ = 1^
- 1v*1v = 1^
- 1v*1^ = 1v
- 2^*2^ = 4^
- 2v*2v = 4^
- 4v*3v = 12^
- 3v*4v = 12^
- 3v*4^ = 12v
- 4^*3v = 12v
- In R1 math multiplication is commutative
- (2v*4^)*3v = 8v*3v = 24^
- 2v*(4^*3v ) = 2v*12v = 24^
- (4v*3v)*2^ = 12^*2^ = 24^
- 4v*(3v*2^) = 4v*6v = 24^
- In R1 math multiplication is associative
- 5v(6^ + 3v) = = 5v*3^= 15v
- = 5v*6^ + 5v*3v = 30v + 15^= 15v
- Multiplication is distributive
- 2^*3v*4v = 24^ = 6v*4v = 24^
- 2v*3^*4^ = 24v = 6v*4^ = 24v
- (2^ + 5v)*(2^ + 5v) = 3v*3v = 9^
- = 4^ + 10v + 10v + 25^ = 9^
Multiplication using Flip Sign
A flip sign in front of an Opposite Value means that the Opposite Sign should be changed to the other Opposite Sign before multiplication.
- –4^*3v = 4v*3v = 12^
- 4^*–3v = 4^*3^ = 12^
- 4^*–3^ = 4^*3v = 12v
- –4^*–3^ = 4v*3v = 12^
- Note: Two flips cancel
Multiplication with Counters
- 2*2^ = 4^
- 2*2v = 4v
- 3*(6^ + 2v) = 12^
A flip sign in front of a Counter means that the Opposite Sign should be changed to the other Opposite Sign after multiplication.
- –1*1v = 1^
- –2*2^ = 4v
- –2*–2*2^ = 8^
- Note: Two flips cancel
- –3*(6^ + 2v) = 12v
Counters cannot be multiplied by themselves because the result of any calculation must be an Opposite Value. So 3*5*2^ = 30^ 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 simple R1 multiplication with our online calculator.
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