Posted by: Alexandre Borovik | December 9, 2011

## A tale about long division

… as told by me, last week, to my students.

An innumerate executor of a will has to divide an estate of 12,345 pounds between 11 heirs. He calls  a meeting and tells the heirs: “The estate is about 12 grands, so I wrote to each of you a cheque for 1,000 pounds.”

The heirs answer: “Wait a second. There is more money left” — and write on the flip chart in the meeting room:

“Ok” — sais the executor – “there are about 13 hundred left. So I can write to each of you a check of 100 pounds”:

“But there is still money left in the pot” — shout the heirs and write:

“Well,”–  says the executor, — “it looks as if I can give extra 20 pounds to each of you”:

“More! More!” — the heirs shout. “I see” — said the executor — “here are 2 pounds more for each of you”:

“I deserve to get this remainder of 3 pounds and buy myself a pint. And each of you gets 1122 pounds”:

After finishing my tale on this optimistic note, I commented that the whole calculation, which looks like that:

is usually written down in an abbreviated form:

And we say that

12345 gives upon division by 11 the quotient 1122 and the remainder 3

which means

$12345 = (11 \times 1122) + 3$

As simple as that.

## Responses

1. What a lovely demonstration! See, long division makes perfect intuitive sense–it’s not just an algorithm to be memorized!

I don’t often have the need to explain long division, but I’ll remember this example for the future.

2. Thank you for sharing this “dissection” of the long division algorithm. I plan to share it with my student teachers next semester.