Definition
Flipping is the specific rotation of an Opposite Value in R1 to its equivalent with the Opposite Sign changed.
Flipping Opposite Values in R1
Multiplication uses the flip sign as follows.
- 1v*–1v = 1v*1^ = 1v
- 4^*–3v = 4^*3^ = 12^
Take 4^*–3^: This equals 4^*3v that results in 12v, alternatively, equals –(4^*3^) = –12^ = 12v.
Next, take 4^*–3v: This equals 4^*3^ and results in 12^, or, alternatively, it equals –(4^*3v) = –12v = 12^.
Finally, take –4v*3v: This is equal 4^*3v and results in 12v, or, alternatively, it equals –(4v*3v) = –12^ = 12v.
Flipping Counters in R1
- –4*3v = 12^ because the Counter contains a flip that applies to the result.
- –4*3^ = 12v because the Counter contains a flip that applies to the result.
Two Counters with flip signs cancel out.
- –4*–2*3v = 24v
Flipping Terms in R1
Work out the Opposite Value of a term before the flipping takes place, except where two flips happen together and cancel each other out. For example:
- – –a = a Note the Opposite Sign of the term a is not known
- √– –a2 = √a2 = a^ or av, as the two flip signs cancel out.
- –2*–2*a = 4a
Where a term is in the form (c + –d)x, c and d are Counters and x is a variable, then multiply the term, x, by the difference between c and d.
If d > c, then the result of the multiplication needs to be flipped. For example:
- (4 + –8)*3v = –4*3v = 12^
In the following example d < c, so no flipping is required:
- (4 + –2)*3v = 2*3v = 6v
More Examples
–ab = a–b
- –4^*3v = 4v*3v = 12^ = 4^*–3v = 4^*3^ = 12^
- –4^*3^ = 4v*3^ = 12v = 4^*–3^ = 4^*3v = 12v
- –4v*3v = 4^*3v = 12v = 4v*–3v = 4v*3^ = 12v
a–b = –ab
- 4^*–3v = 4^*3^ = 12^ = –4^*3v = 4v*3v = 12^
- 4^*–3^ = 4^*3v = 12v = –4^*3^ = 4v*3^ = 12v
- 4v*–3v = 4v*3^ = 12v = –4v*3v = 4^*3v = 12v
–a–b = ab
- –4^*–3v = 4v*3^ = 12v = 4^*3v = 12v
- –4^*–3^ = 4v*3v = 12^ = 4^*3^ = 12^
- –4v*–3v = 4^*3^ = 12^ = 4v*3v = 12^
Conclusion
Try these examples of R1 flipping with our online calculator.
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