Division is a completely different set of tricks to multiplication, but once again you only need to know the process, and not actually have any times tables or understanding of what's happening, to make it work. To divide, we just take away multiple times. You did practise your taking away, didn't you?
Let's start with 56 / 7. If you know your 7 times table, you will know the answer. Can we get it with a counting cloth? Lay it out, number to divide into on the left, number we are dividing by on the right:
We want to use the third column to keep count how many times we have done the take away. While you are learning, tap the counters from the right hand column, while you match and take away from the left. You need to keep the red counters where they are so you don't forget what you are dividing by.
We need to untidy the left column to make it easier to do the take away.
Now we can take away. Take 7 from the left, and put 1 counter on the 3rd column's 1s row to show we've taken away one 7.
Again. Take 7 from the left, and put 1 counter on the 3rd column's 1s row to show we've taken away two 7s.
Again. Take 7 from the left, and put 1 counter on the 3rd column's 1s row to show we've taken away three 7s.
Again. We need to untidy first, then take 7 from the left, and put 1 counter on the 3rd column's 1s row to show we've taken away four 7s.
Again. Take 7 from the left, and put 1 counter on the 3rd column's 1s row to show we've taken away five 7s.
Again. Untidy, then take 7 from the left, and put 1 counter on the 3rd column's 1s row to show we've taken away six 7s.
Again. Take 7 from the left, and put 1 counter on the 3rd column's 1s row to show we've taken away seven 7s.
Finally, take 7 from the left, and put 1 counter on the 3rd column's 1s row to show we've taken away eight 7s, and there is nothing more to take away from.
We need to tidy up our count, but there we have our answer. 7 goes into 56 eight times, or 56 / 7 = 8.
What happens when we have counters left? We have a remainder; it actually remains in place on the board.
Lay out 83 / 20
Take away and count
And our answer is 20 goes into 83 four times, with 3 left over.
Yes ,division and multiplication ARE tedious. No wonder pen reckoning took over!
I find it quite fascinating that the terms "take away", "remainder" and the comma in 1,000 come from such an old system, in use over 5 centuries ago.
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