Figuring out division problems can often be challenging when dealing with larger numbers. Once you memorize multiplication tables, any division problem whose dividend is an answer within the multiplication table for the divisor is pretty simple. For example if you have the problem 72 ÷ 8 , you can think what multiplied by 8 gives 72?... 9 of course! Once you start dealing with bigger dividends this is not so easy. Lets take the problem 865 ÷ 9 as an example. There are some different methods to solve this problem, but the most common way for humans to solve it is using long division.
First we must write the problem in the following form:
Our first step involves looking at the divisor 9. We start with the left most digit of our dividend 865...in this case 8. If 8 is larger than 9 then we can continue, if not we must move to the next digit. In this case since 8 is smaller than nine, we move to the next digit of 6. We now put those digits together to see if 86 is larger than 9. Since it is we can continue.
We now have the smaller division problem to deal with 86 ÷ 9. If we know our multiplication tables we know that 86 cannot be divided by 9 cleanly so we look for the closest result that is less than 86, in this case 9 x 9 = 81 so we will use 9 as our answer. We write the 9 (our answer for this portion of the problem) above the right most digit that we used.
We now multiply our answer for that part of the problem in this case 9, by the divisor, which in this problem is also 9
9 x 9 = 81.
We put the 81 below the digits we used for this part of the problem, in this case under the 86.
Our next step is to subtract 81 from 86. If our answer from this subtraction is greater than the divisor, we need to go back and increase our answer to the first division part of the problem. In this case 5 is smaller than 9 so we are ok.
86 - 81 = 5
We write our answer below the 81 just as we would in a normal subtraction problem.
We have now found the first digit to our answer. We must now repeat this procedure for the rest of the digits in the dividend. We do this by taking the next digit, in this case 5 and dropping it down next to the result of the subtraction portion of the last part of the problem.
We can now determine how many time 9 goes into 55 or 55 ÷ 9. The closest match we have is 6 since 9 x 6 = 54. We can now write the 6 above the 5 in the answer.
Multiply 6 x 9 to get 54 and write it below the 55.
Subtract 55 - 54 =1
At this point we would want to drop down another number to continue. However we cannot since there are no more digits left to drop down. If the result of our subtraction was 0, then we would be done and our answer would be 96. In this particular case we are left with a 1. That 1 becomes the remainder.
We finally reach an answer of
865 ÷ 9 = 96 r1.