I’m trying to get my child to do long division. The question is 414 divided by 23. We got to 184 divided by 23, and he freaks out. How do I show him the easiest way to work it out?
The fact that you got to 184 is good.You got the basics, and you are definitely on the right track.For good measure, where does 184 come from ? When we are doing long division by a 2 digit number, we start with the number formed by the first 2 digits, in this case 41. How many times does 23 fit into 41 ? Answer 1 , 41-23 =18 , lower 4 (the 3rd digit of 414) and you get 184.The difficulty when you are doing long division and dividing by a two digit number is that you have to find the answer to :how many times does the divisor (here, 23) fit into the remainder (here, 184) ?We know that the answer must be one of the numbers 0, 1, 2, 3, .. to 9. Yes, each time there are 10 possibilities. We have to find the largest number between 0 and 9 so that this number multiplied by the divisor (here, 23) fits into the remainder (here, 184).How do we do this ? We could calculate the 10 multiplications, but that is too much work. Instead we proceed by trial and error and estimation.So how do we estimate ?there are a few possibilities :we leave the last digit out, for both the remainder and the divisor, so instead of looking at 184 and 23 we look at 18 and 2 , this is easier, because we know our multiplication tables, and we know 2 fits 9 times into 23. so our first estimate is 9.we can also round the numbers. For instance 23 is close to 25, and 25 is a fun/easy number : the multiplication table of 25 is : 25, 50, 75, 100, 125, 150, 175, 200, 225, 250. See the pattern ? It’s easy , 25 fits 7 times into 184. so now we have a second estimate : 7.now it takes some work , we have to multiply 23 by 7, 8 and 9 and see which one of these three multiplication results fits best into 184. Sometimes it is good to do these trial multiplications on a separate sheet. So let’s do it : 23*7 = 161, 23*8=184, 23*9=207 , In this case, 8 is the answer.So the division of 414 by 23 is 18. Well done !.Unfortunately, there is no way around this trial and error / estimation step. The more you do it, the better you get at it. In this case, having calculated the result for 7 and 8, it would have been obvious that the calculation for 9 would not be necessary anymore. In general, when you get good at long division, the estimation is usually limited to 2 trials for each remainder.All the best !