how to find 2/7 mod 12?

Question

with fractions how to take mod 12?

Answer 1

2/7=x is the same as asking 2=7x



So you need to find an x such that 7 times x is something that reduces to 2 mod 12.



What reduces to 2 mod 12? 2, 14, 26, 38, etc... are any of these divisible by 7? Right away you can see the answer: since 14 is divisible by 7, you can use this to find your answer.



14=7*2, which is congruent to 2 mod 12.

So 2=7*2 mod 12



So 2/7=2 mod 12

Answer 2

There are at least a couple of ways to reasonably define this; Nameless has one of them:

(x/y) mod b,

meaning to find an integer c such that

x = (y*c) mod b.



This won't always possible if y and b are not relatively prime. For instance

5/6 mod 12

won't have an answer, because no integer multiple of 6 can ever be = 5 mod 12.



Here's another possible definition.



When you take a mod b, where a and b are positive integers, with b≠0, you are solving this equation for r:

a = b*q + r,

where q is an integer, and

0 ≤ r < b



This is known in mathematics as the "division algorithm," with:

a = dividend

b = divisor (which is not allowed to = 0)

q = quotient

r = remainder



This definition can be extended in a couple of ways -- to negative numbers, and to real numbers, a, b, and r, but always with the proviso that q must be an integer, and that b≠0. For b < 0, the constraint on r becomes:

b < r ≤ 0



Under this definition,

2/7 mod 12 = 2/7

[2/7 = 0*12 + 2/7; 0 ≤ 2/7 < 12]



This is essentially Carlos B's answer. You can also get



5/6 mod 12 = 5/6 [5/6 = 0*12 + 5/6; 0 ≤ 5/6 < 12]

-5/6 mod 12 = 67/6 [-5/6 = -1*12 + 67/6; 0 ≤ 67/6 < 12]

125/6 mod 12 = 53/6 [125/6 = 1*12 + 53/6; 0 ≤ 53/6 < 12]

12 mod (2/7) = 0 [12 = 42*(2/7) + 0; 0 ≤ 0 < 2/7]

12 mod (5/7) = 4/7 [12 = 16*(5/7) + 4/7; 0 ≤ 4/7 < 5/7]

12 mod (-5/7) = -1/7 [12 = -17*(-5/7) + (-1/7); -5/7 < -1/7 ≤ 0]

etc.

Answer 3

2/7 mod 12 means that the remainder is taken as the answer and not the quotient.

therefore

2/7/12 = 2/7*12 which comes out to be 2/84 which when simplifies is 1/42.



when 42 is divided by 1 then the quotient is 0 as 42 times 0 gives zero which has to be smaller than dividend 1. when 0 is subtracted from 1 then the remainder is obviously 1....



therefore 2/7 mod 12 = 1

Answer 4

Well, although mod is applicable on integers, to solve your question I'll apply the mod definition in strict sense:



"a mod b is the remainder of the division between a and b"



if you divide 2/7 by 12 it gives you 0 as quotient and 2/7 as remainder, which would give my final answer:



2/7.



Update: Try 2/7 mod 12 using windows calc, it throws 2/7



press 2 / 7



then press mod



press 12, bingo! , you'll get 2/7