Question

is 50*2+25-10MOD4+10 the same as
(50 2+25-10) mod (4+10) ????

Answer 1

that notation is a little weird. why would someone write mod (4+10) and not mod 15?

Answer 2

Usually when you are working with modular arithmetic, you have to mod the entire statement. It doesnt make any sense to only look at a portion of the statement.

Answer 3

so before you do MOD you need first solve the other operations?

Answer 4

why is it 20MOD110 is 20?

Answer 5

you can go either way. Do all the operations first and then mod, or mod completely first, then do operations. just dont mix up the two.
and yes, 20 mod 110 is 20.

Answer 6

how?20 mod 110 is 20

Answer 7

could you show the solution

Answer 8

There are a couple of ways to see it. One way to think of x mod 110 is what is the remainder when i divide by 110? well 20 is already less than 110, so its remainder would be 20. Another number equivalent to 20 mod 110 is 130. Because when i divide 130 by 110, i get a remainder of 20.

Answer 9

what?
i already know that MOD is the remainder in division
but i can't understand how you divided 20 to 100
sorry if i did'nt understood your explanation

Answer 10

are we working with 100? or 110?

Answer 11

110

Answer 12

typo :)

Answer 13

you would divide 20 by 110. The answer is 0 with a remainder of 20. Or you can write out 20 using the division algorithm:
20 = 0*110+20
The remainder is 20 so 20 mod 110 is 20. In fact any number that is less than 110 will be equivalent to itself.
35 mod 110 is 35. 109 mod 110 is 109. etc.

Answer 14

could you show me on how you divide 20 by 110 and get 20?

Answer 15

you are getting a remainder of 20. Not 20.

Im not saying:
\[\frac{20}{110} = 20\]
thats wrong.
Im saying:
\[\frac{20}{110} = 0+\frac{20}{110}\]
so the remainder is 20.

Answer 16

if i did 130 it would be:
\[\frac{130}{110} = 1+\frac{20}{110}\]
so the remainder is 20.
so 130 mod 110 = 20

Answer 17

yup saying it to remainder

Answer 18

how did you get remainder 20?

Answer 19

sorry if i can't really understand

Answer 20

Maybe its because we are working with big numbers.
Could you tell me what the remainder is when i divide 15 by 6?

Answer 21

is my insight correct that if the left part of the mod is less than the right part, the mod will always be the left part?

e.g
30mod3425234534
mod will be 30?

Answer 22

yes that is right. You need to be able to calculate remainders though. otherwise if the number is bigger than the mod you wont know how to work it out.

Answer 23

because mod is always 30 in wolfram alpha if i enter a larger number on the right side of mod

Answer 24

so 60mod26283475908273459082734509287345(or whatever number but larger than 60) the Mod will always be 60?

Answer 25

yes

Answer 26

thanks