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mental calculations

Posted By: Chuck Bower
Date: Saturday, 9 June 2007, at 1:31 p.m.

In Response To: Online Tournament (Klaus Evers)

what is the most efficient way to calculate (e.g.) 6.5/26.5 OTB?

Multiply numerator and denominator by 2 giving 13/53. From here you can go different ways. One way is to notice that 13/52 (a bridge hand :) is 1/4 or 25%. Continuing, the actual denomintor is 1/52 or about 2% more, so you can correct the answer (25%), lowering it relatively by 1/50 or half a percent, giving 24.5%.

The second method is to multiply num. and denom. by an integer that gets you close to 100. Here multiply 13/53 by 2/2 giving 26/106. Now you want to again correct denominator and numerator by same amount. Denom is high by 6% which (again recognize) is 1/16. So denom is (17/16) meaning you should multiply num. and denom. by 16/17. You know that the denom will then be 100 by construction, so the numerator * (16/17) is the answer. But again, you don't have to multiply it all out. You want to lower the numerator by 1/17. That is, the answer is the current numerator (26) minus 26/17. The latter is 1 9/16 or about 1.5. 26 - 1.5 is 24.5%. (And luckily this agrees with the earlier answer found by the other method. :)

This actually goes a lot faster in your head (with practice) than does writing out or even reading the explanation (thank goodness).

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