Long Division Made Simple

Recently, after An Explanation of the Inner Workings of Name Servers And The Squirrels Within, Cream Until Fluffy asked me to explain long division.

Long division requires a rather different sort of animal. You need burrowing, ground dwelling mammals, rather than arboreous squirrels. I like to use marmots or maybe rabbits if no marmots are available. You can need quite a lot, so find a well populated burrow.

For this example we will divide 38653 by 17, as this comes up quite often, and I'll be using marmots.

‘Hello, I’m a marmot’

We start with the first digit of the number we want to divide: 3.
Stand near a burrow and entice three marmots out. When they surface, ask them to gather in groups of 17. In this case they will scamper around being confused, because there are not enough to form a group, so send them back.

Try with the first two digits: 38.
Summon 38 marmots, and tell them to group as before. This time you will see two groups, sitting neatly, and four marmots will be scampering around in confusion.
Write down the number of groups (2) above the 38 bit of the 38653, and the number left scampering (4) beneath. Thank them and send them back.

These poor, agitated fellows couldn’t make a full group.

Next to the 4, write down the next digit in the big number: 6, so now ask for 46 of your furry helpers to come up, and form groups, once again, of 17. There will be two groups, so write a '2' above the 6 in the 38653. The number of confused marmots might be hard to see, as there are quite a few, so send the two groups back first, then send the remainders back one by one, counting them as you go. You should count twelve. So write 12 below the '6' bit of the 38653.

Now we need the next digit: 5. Write that next to the 12 to make 125. That's quite a lot of marmots, so it might take a while, but you will find they make seven neat groups, who will sit patiently, leaving six who are quite out of sorts trying to arrange themselves as a group. So write '7' above the 5 in the 38653, and the '6' beneath. Thank them, and ask them to return underground.

Write the last digit: 3 next to the 6 to give 63, and so request 63 cuddly rodent troglodytes and ask, for the last time, that they form the groups. You will see three neat, happy groups, so write three above the last digit. Count off the remaining 12 as they go back in the burrow.

‘Are we done yet?’

You should see the number 2273 written above the 38653, and a 12 as the last remainder beneath, this is because 38653 divided by 17 is 2273 with 12 remaining!

If you add '.000' after the '38653' you can carry on bringing down the zeros after the reminders, and, by grouping and counting as before, we find the answer to three decimal places is 2273.705 with 13 remaining. If after the last set, the number of remaining marmots is more than half a group (if you ask one nicely, they will usually tell you if this is the case, but it is not too hard to work out) you can round up the last digit. In this case 13 is more than half 17, so we round up to 2273.706.

I always carry a big bag on pine nuts as a 'thank you' treat or two bags if I'm doing decimal places.

They always seem to make this so difficult in schools, but it really is that simple.

Do not ask this one.