you take the inverse of 1/4 which is 4 and ask yourself

4a = x where x mod 27 = 1 I'm looking for a number from 1 - 27 for 'a' and a value that works is 7 because 4*7 = 28 and 28 mod 27 = 1

for 1/4 = b mod 9

4b = x where x mod 9 = 1 what are the numbers that x mod 9 = 1 .... 10, 19, 28, 37, etc to 73 after that b becomes greater than 9.

The only number evenly divisible by 4 is 28 so b must be 7

http://mathworld.wolfram.com/ModularInverse.html

http://en.wikipedia.org/wiki/Modular_multiplicativ...

got it.

1/4 = b mod 9

1 mod 9 is equiv 10 is equiv 19 is equiv 28

1/(1/4) is a factor of 28 so 4*b = 28, b =7

then you have 4*7 is equiv 1 mod 9.

so basically what I did was modulo division. 4/4*7 is equiv 1*1/4 mod 9

using same process for original question.

1 mod 27 is equiv 28

4*7 = 28

4*7 is equiv 1 mod 27

using division rules

4/47 is equiv 1/4 mod 27

if something is equiv, that says

1/4 mod 27 is equiv a, and

1 mod 27 is equiv 1/4

a = 7