Changing Numbers To Prescribed Values Under Special Limitations

[allo]

x=1825+91/1217

y=7+2/3

z=1827+2/3

Is there any way to turn x into z only using the first two terms, andor a constant, and the operators ' + ', ' - ', ' * ', ' / '.

I know I can take ((x)-(x mod 10)) + y = z, but this uses a modulus.

... Basically the core of the question is can I change any number's last digit and its decimal value to something I decide by only using the number itself and the desired digit and decimal?

I feel like splitting the numerator and denominator and running independent operations on each might be the way to go.

 

[mfb]

1217x = 2221116
3y = 23
As those do not have a common divisor (apart from 1), you can find integers q,r, such that qx+ry=1. That can be written with a long series of "x+x+x+... -y-y-y-..." (or vice versa), of course, so you do not need q and r.
In the same way, you can get 1820. Add y and you are done.

andor a constant

? If you can use the constant z/x, it is easy.