# When you divide by 3 can there be a remainder of 5?

###### June 01, 2014 4:31AM

No.

The remainder after any division must be less than the divisor: it can be any of the numbers 0 to the divisor less 1.

For three: 3 - 1 = 2, so the possible remainders are: 0, 1, 2

Division is the opposite of multiplication in that it tells you how many times the divisor can be subtracted from the dividend to get to 0 without going past 0; if there is a remainder, it tells you that you that a fraction of the divisor needs to be subtracted to get to 0.

eg 12 ÷ 3 = 4 says that you can subtract 3 from 12 four times and you will get 0: 12 - 3 (once) = 9, 9 - 3 (twice) = 6, 6 - 3 (three times) = 3, 3 - 3 = 0 (four times).

eg 11 ÷ 3 = 3 remainder 2 says that you can subtract 3 from 11 three times but if you subtract it four times you will go past 0: 11 - 3 (once) = 8, 8 - 3 (twice) = 5, 5 - 3 (three times) = 2; but 2 - 3 = -1 which is past zero, so there is a remainder of 2 which requires a fraction, in this case two thirds of 3, to get to (exactly) zero: 2 - 2/3 x 3 = 2 - 2 = 0.

If you have a remainder larger than the divisor, you can subtract the divisor again and still not reach 0 (as in the "once", "twice" and "three times" of the examples above).