Long Division - Why and How

Long Division troubled me when I was at School - it was just plain confusing !

Until I realised it was just some way to get an answer. Not the only way, but one that works well if followed well. In other words, just follow the steps and *magic* it works!

So, what is it trying to solve? Answer: Difficult division problems !

Division vs Long Division

We don't need it for 42 ÷ 6 Which is 7 of course. Because 6 x 7 = 42 (look up your times tables if you don't believe me!)

But what is 462 ÷ 6 ? Hmmm, not so easy.

We could try guessing ... Is it 100? ... 100 x 6 = 600. No too big.

Is it 50? ... 50 x 6 = 300. Too small ... somewhere in between

Is it 75? ... 75 x 6 = 450. Close! Nearly 462. Let us try creeping up

Is it 76? ... 76 x 6 = 456. No, not yet ...

Is it 77? ... 77 x 6 = 462. BINGO!

But what if the problem is even more difficult, say 7,698 ÷ 6 ? That is going to take a LONG time to guess, so along comes Long Division to help us ...