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Three Sevenths

And discovering the beauty of decimals...

The other day I innocently asked a primary school teacher when his top set class of ten- and eleven-year-olds might be expected to work out 3/7 (three sevenths) as a decimal.  His answer surprised me: "For that sort of difficult fraction, I would expect them to use a calculator".

I like calculators. They are a vital way to take the drudgery out of big calculations. But three-sevenths does not come into the category of big calculations.

A very crude straw poll of teachers suggests well under 5% (i.e. only the tiniest minority) of Year 6 primary children know the method for working out 3/7 as a decimal.  

OK, many will say, but what harm is there in (a) waiting until secondary school to learn this, and (b) using a calculator.

Here are my three reasons:

  1. If you can work out fractions like 3/7 without a calculator, you have the foundations for an important life skill: the ability to make quick estimates of percentages in your head. (3/7 is about 0.43, a bit more than 40%).
  2. The process of working out 3/7 leads children to discover a pattern, and isn't that a key part of what maths should be about? (The decimal starts 0.428571... and then the pattern 428571 repeats forever.  A calculator display isn't long enough to reveal this.)
  3. Working out 3/7 is NOT DIFFICULT, for a significant portion of primary children at least. In fact, many find it quite a fun exercise.

I'm not saying every child should be expected to be able to work out 3/7 as a decimal.  Many children never really grasp the idea, however much they practise it and however old they are.  But by the age of nine or ten, many children are more than capable of grasping the method very quickly, and those children are missing out if they don't at least get exposed to it in primary school, so they have a chance to add it to their toolbox of handy numerical methods. 


Here's how I do it, using short division (maybe you do it differently):

                 0 . 4 2 8 5 7 1 4.... 

            7 ) 3 . 0206040501030...

The script that runs through my head goes: "7 into 30 goes 4 times (write 4 above), remainder 2, carry  that 2 across,  then 7 into 20 goes  2 times (write 2 above) carry 6, then  7 into 60 goes 8 times (write 8 above)...." and keep going.