George, it makes no sense to write "19/5 = 3 mod 4." I take what you mean is that 5 goes into 19 three times with a remainder of 4, but that's not what the "mod" notation means. If you want to write that 19/5 is 3 remainder 4, you should just write "19/5 = 3 r4."

The "mod" notation is used as follows: if a, b, and c are integers, then "a = b mod c" means that "a - b is divisible by c" -- or, if b is between 0 and c-1 inclusive, you can interpret this as saying "a has remainder b when divided by c."

That's why "19/5 = 3 mod 4" makes no sense: first, you can use a rational number in a "mod" statement, and second, it looks like you're saying the number has remainder 3 when divided by 4.

The write way to use mod notation here would be to say "19 = 4 mod 5" (in other words 19 has remainder 4 when divided by 5). The mod notation doesn't take into account how many times c actually goes into a.

## Comments

Thank you!

George, it makes no sense to write "19/5 = 3 mod 4." I take what you mean is that 5 goes into 19 three times with a remainder of 4, but that's not what the "mod" notation means. If you want to write that 19/5 is 3 remainder 4, you should just write "19/5 = 3 r4."

The "mod" notation is used as follows: if a, b, and c are

integers, then "a = b mod c" means that "a - b is divisible by c" -- or, if b is between 0 and c-1 inclusive, you can interpret this as saying "a has remainder b when divided by c."That's why "19/5 = 3 mod 4" makes no sense: first, you can use a rational number in a "mod" statement, and second, it looks like you're saying the number has remainder 3 when divided by 4.

The write way to use mod notation here would be to say "19 = 4 mod 5" (in other words 19 has remainder 4 when divided by 5). The mod notation doesn't take into account how many times c actually goes into a.

There's a typo in my comment that I can't edit to fix: it should say "

first, you CAN'T use a rational number in..."