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Ling Min Hao
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Is 23 = 5(-4)-3 gives a remainder -3 when divided by 5 ? is this statement true ? some of my colleagues said that remainder cannot be negative numbers as definition but I am doubt that can -3 be a remainder too?
Usually we consider entire equivalence classes in such cases: Every single element of ##\{\ldots -13, -8, -3, 2, 7 , 12, \ldots\}## belongs to the same remainder of a division by ##5##. We then define all five possible classesLing Min Hao said:Is 23 = 5(-4)-3 gives a remainder -3 when divided by 5 ? is this statement true ? some of my colleagues said that remainder cannot be negative numbers as definition but I am doubt that can -3 be a remainder too?
mfb said:The remainder is usually required to be between 0 and N-1 inclusive. 23 and -2 (not -3) are in the same equivalence class. This can also be written as 23 = -2 mod 5.
"-23 divided by 5 is -4 with a remainder of -3". I would consider that statement true.Ling Min Hao said:Sorry it should be -23 = 5(-4) - 3 , so in conclusion is, this statement true ?
"Positive or negative remainder" refers to the result of a division operation where the remainder can be either positive or negative. The remainder is the amount left over after evenly dividing the dividend by the divisor.
The calculation of "positive or negative remainder" is based on the modulus operator (%). This operator returns the remainder of a division operation, taking into account the signs of the dividend and divisor. If the remainder is positive, it means that the dividend was larger than the divisor and there is still a portion left to be divided. If the remainder is negative, it means that the dividend was smaller than the divisor and there is no remainder left.
Yes, the remainder can be zero in "positive or negative remainder" if the dividend is evenly divisible by the divisor. In this case, the remainder is neither positive nor negative.
"Positive or negative remainder" can be used in various real-life scenarios, such as calculating change in a transaction, determining the number of items left over after dividing them into equal groups, or finding the number of days remaining in a month or year.
The difference between "positive or negative remainder" and "absolute remainder" lies in their interpretation of the remainder. In "positive or negative remainder", the remainder can be either positive or negative, depending on the signs of the dividend and divisor. In "absolute remainder", the remainder is always positive, as it represents the absolute value of the leftover portion after division.