Why do you always subtract in division?

Answer 1

Without going into the intricacies of long division........ Division is successive subtraction as opposed to multiplication which is successive addition. Let's say you want to divide 19 by 3, in successive subtraction you would first see if you can take away 3 from 19. The answer is yes. So you take away 3 and create a variable called quotient (which initially has a value of 0). Since you were able to successfully take away 3 from 19 during this first attempt, increment the quotient by 1. Since you took away 3 from 19 and accounted for it in the quotient (which is the number of times you are able to successfully take away 3 - the divisor) see what is left in the original number. 19 is now 16. Can you take away 3 from 16. The answer is yes. Increment the quotient - now it should be 2 and 16 will become 13. Keep doing this. You will see that you can do this six times in all (the quotient will have incremented to 6) and then you will be left with 1 from which you cannot take away 3. If you are limited to just integer division the process ends here. Of course if one knows multiplication tables, then this problem can be solved in one step. One would know that 3 can be taken away from 19 six times with a remainder of 1 at the end. So to illustrate this further, if we started with 19 pencils and the teacher wanted us to make bundles of 3 pencils, division or successive subtraction tells us that we can make six bundles with 1 pencil left over.