Can remainder be negative?

[srisl11]

There are different opinions regarding remainder in the following post
https://www.beatthegmat.com/remainder-y-3-t23172.html

Can someone please clarify whether remainder can be negative?



I read the definition in https://en.wikipedia.org/wiki/Remainder
but still unclear...
Please help

[uttara]

this is from GMATPrep:

Quotients and remainders
If x and y are positive integers, there exist unique integers q and r, called the quotient and remainder, respectively, such that y = xq + r and 0 &#8804; r < x. For example, when 28 is divided by 8, the quotient is 3 and the remainder is 4 since 28 = ( 8 ) (3) + 4. Note that y is divisible by x if and only if the remainder r is 0; for example, 32 has a remainder of 0 when divided by 8 since 32 is divisible by 8. Also note that when a smaller integer is divided by a larger integer, the quotient is 0 and the remainder is the smaller integer. For example, 5 divided by 7 has the quotient 0 and the remainder 5 since 5 = (7)(0) + 5.

[srisl11]

[quote="uttara"]this is from GMATPrep:

Quotients and remainders
If x and y are positive integers, there exist unique integers q and r, called the quotient and remainder, respectively, such that y = xq + r and 0 &#8804; r < x. For example, when 28 is divided by 8, the quotient is 3 and the remainder is 4 since 28 = ( 8 ) (3) + 4. Note that y is divisible by x if and only if the remainder r is 0; for example, 32 has a remainder of 0 when divided by 8 since 32 is divisible by 8. Also note that when a smaller integer is divided by a larger integer, the quotient is 0 and the remainder is the smaller integer. For example, 5 divided by 7 has the quotient 0 and the remainder 5 since 5 = (7)(0) + 5.[/quote]


According to the definition if both divisor and dividend are +ve , then remainder is +ve...
But what if either the divisor or dividend is negative?

[vishubn]

THis post as well talks about remainders !!
and yes remainders can be negative

https://www.beatthegmat.com/remainders-t23169.html

vishu