# Changing Numbers To Prescribed Values Under Special Limitations

$x = 1825 + \large \frac{91}{1217}$

$y = 7 + \frac{2}{3}$

$z = 1827 + \frac{2}{3}$

Is there any way to turn $x$ into $z$ only using the first two terms, and/or 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.

-
You say you're allowed to use a constant, so why don't you just calculate $z-x$ and then add that constant to $x$? – Gerry Myerson Feb 9 '13 at 11:50
I'm sorry, I misspoke in the question... you can only use the first two terms and a constant. – Peregrine Feb 9 '13 at 11:55
@Perry: That doesn't answer Gerry's objection at all. – Chris Eagle Feb 9 '13 at 12:53
Gerry uses the z term. $z-x$. The problem, though I mispoke it before Gerry's suggestion, states you can only use the terms x and y and a possible constant. – Peregrine Feb 9 '13 at 12:58

## 1 Answer

$z=x+y-5\frac{91}{1217}{}{}{}{}{}$

-