I thought I was pretty good at doing math in my head until yesterday I saw someone do $17.4/4$ in their head, without writing anything down and it took them less than 20 seconds.
What do you do to do this in your head? Even with the answer of 4.35 I could not work backwards to the right answer. I thought maybe if you break the problem up into $16/4=4$ which leaves $1.4$ so to get 1.4 from 4 you have to just get a fraction of 4. Half of four is too much, 1.3 of four is too small. So now I know that the answer is somewhere between $1/2$ and $ 1/3$ but from here it seems like it would get even more complicated. Would I just want to determine that a tenth of four is .4 and then add that to the final answer? I have no idea and this seems to be too much to do in my head.
Best Answer
As you said, notice that 17.4 = 16 + 1.4, and the only hard bit is to calculate 1.4 / 4
To divide 1.4 by 4, use the fact that dividing by 4 is the same as dividing by 2 twice. If you divide by 1.4 by 2 once, you get 0.7. If you divide by 2 again, you get 0.35, so the answer is 4.35
It might help, when dealing with decimals, to multiply them by a power of 10 in your head before doing the division. For example, when calculating 1.4 / 2 I mentally convert that to 14 / 2 (which is 7) and then divide by 10 again to get 0.7
Now to do 0.7 / 2, I multiply by 10 to get 7 / 2 (which is 3.5) and then divide by 10 to get 0.35