I understood that for a direct proportion such as "if 6 mangoes cost $12, then how many dollars worth are 12 mangoes?", we have to first divide 12 by 6 to get the no. of divisions of 6 in 12 i.e. precisely 2 and then as 1 division is worth $12 we multiply the two divisions with $12 and that's how we get $24. What I don't understand is that for an inverse proportion such as "there are a certain no. of pills and for 10 patients the pills will last for 14 days, for 35 patients how long will the pills last?", the no. of days will obviously decrease and hence more the patients less the no. of days, but to calculate the answer we divide and not multiply as we do in direct proportion question such as the one above (we multiplied 2 with 12). Why do we divide to find the answer in inverse proportion? Why can't it be subtract or add or any of those things. What I mean is that what is the logic behind the last division? Thanks!