This is a question for a 5th grade math problem. My sister needs help estimating a division problem with a remainder.
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The purpose of the estimate is not to get an accurate answer, but just an indication of what the answer should be approximately, so that when the actual answer is determined, you can compare it with the estimate. They should be fairly close. If they are, this gives you confidence in your ability to work out the answer. If they're not, you may have made a mistake in your calculations. With practice, you become used to estimating quickly and that gives you a rough expectation of what the answer should be. So when you're doing a division it's not the remainder you need to be concerned about, but rather a rough idea of what the answer is going to be when calculated thoroughly. For example, if you were asked to divide 490 by 21, you could quickly estimate this by using 500 in place of 490 and 20 in place of 21, because these substitute numbers are close enough, or compatible with the actual numbers. 500 divided by 20 is 25. That can be done quickly in your head. 490/21 is going to be roughly 25. The actual answer is 23 with a remainder of 7. The estimate doesn't try to predict the remainder, but 25 is close enough to 23 to tell you that the real answer is probably correct. If you calculated 490/21 to be something way different from 25, you would suspect something had gone wrong in your calculations. So that's it: the estimate is just a quick fire judgment, before you take the time to do the proper calculation. An estimate is, or should be a quick mental calculation and not a laborious or lengthy exercise.

For some numbers there is a way of predicting the remainder without doing any division at all. The obvious one is dividing by 2, because all odd numbers will give remainder 1. Dividing by 4 requires dividing only the last two digits by 4 and noting the remainder. Dividing by 8 requires dividing the last three digits and noting the remainder. Dividing by 5 is just a matter of noting whether the number ends in zero or 5. If it does there's no remainder; if it doesn't the remainder is found by subtracting 5 or zero from the last digit, depending on the size of the digit. If the digit is between 1 and 4 then so is the remainder; if it's between 6 and 9 then the remainder is found by subtracting 5. When dividing by 9, we don't do any division at all: we simply add up the digits making the number and if the result is 10 or more we add the digits of the result and we keep doing this until we end up with a single digit. If this digit is 9 the number is divisible exactly by 9; otherwise the digit is the actual remainder (this method is not surprisingly called the 9's remainder, and it can be used to check addition, subtraction and multiplication with a 90% accuracy level). Division by 11 is slightly more tricky, but consists of, starting with the last digit, add the alternate digits of the number then subtract the sum of the remaining digits. If the result is positive then that is the remainder; if negative then add 11 to find the remainder; for example, to find the remainder of 98765 divided by 11, we add 5+7+9=21 and subtract 6+8=14: 21-14=7, so the remainder is 7. Another example: remainder of dividing 23451 by 11; 1+4+2-(5+3)=-1+11=10, so the remainder is 10. If the result of the alternate subtraction exceeds 11 repeat the process: 190827 gives 7+8+9-(2+0+1)=21 so the next step is 1-2=-1, add 11=10, so 10 is the remainder.

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