(a long divided by a short anyway)
the main task:
dividing by 4 is the simplest place to start
can students create other numbers so that when you divide by 4 they 'cycle'
[i.e. the lead digit goes to the end]
you can either work backwards or forwards to create these numbers
with division by 4, all of the digits will work as a lead number
there are some patterns to notice, families: starting with 2, 5 and 8 for example
dividing by other numbers is also interesting:
all divisors work (create a cycle)
unfortunately the lengths of the numbers for other divisors are rather long:
- dividing by 2 needs a number that is 18 digits long
- 3 needs 28
- 4 all need 6
- 5 needs 42 apart from the one question (starting with a 7) above
- 6 needs 58 (not really for the faint hearted)
- 7 needs 22
- 8 all need 13
- 9 needs 44
however, this work can be ever so good tables practic
it's interesting, if peculiar
that there is only one six long example for dividing by 5 and the division yields the repeating block for 1/7th as a decimal...
patterns when dividing by 4:
if you chop up the six digit numbers into two blocks of 3
and add them e.g. 205 + 128 you get interesting results
as you do if you chop them into three blocks of 2 and add them
all reminiscent of turning fractions into decimals with prime divisors
Ed Southall has kindly posted some slides for this on his blog
and here's the T shirt:
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