Spring 2021 Calculation Challenge (Division)

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Students who are training in mental calculation often ask me how it’s possible to perform accurate divisions by long numbers, such as:

450 ÷ 34.1826

My preferred method is cross-division, which involves repeated division by a 2-digit number (in this case, by 34) followed by some simple subtractions. The method is fairly straightforward (after some practice), and allows you to obtain arbitrary accuracy.

Here is the full explanation, and worked example, of the cross-division method for dividing by long numbers.

 

Division in Competitive Calculation

The Memoriad competition, usually held every 4 years, includes a category for exact divisions by 5-digit numbers. The world-record holder is Jeonghee Lee, who is 2018 calculated 10 problems of the following format, in under 60 seconds!

7403131344 ÷ 92792

The answer to these questions is guaranteed to be a whole number—in this case, 79782.

Spring Challenge

Now it’s your turn! Using the method linked above (or another method, if you prefer), practise performing inexact divisions (where the answer ends in an infinite decimal) to calculate as many digits of accuracy as possible.

To help you practise, and measure your scores, I’ve provided the testing tool below.

Instructions

  • Set the time limit that you would like. When you start, I’d suggest to set it to “unlimited” to disable the timer.
  • Set the number of digits for the divisor. When you begin, I’d suggest to set it to “5 digits”.
  • Immediately start calculating, typing in the digits as you go. Don’t forget the decimal point!
  • Either when you click [Enter], when you press “Go!”, or when the timer runs out, the tool stops accepting your input, and displays your statistics. The number of digits is usually not a whole number—this is to partially account for questions of different difficulty.
  • To generate a new question, either press “Go!” or change the setting for question length.

Challenge

Submit your best scores by email [admin [at] worldmentalcalculation [dot] com] in the next 30 days, including the following:

  • Question
  • Time (e.g. 60 seconds)
  • Score
  • Screenshot or media (optional)

There is no prize to be awarded—this is for interest, challenge and friendly competition only—but I may publish some of your interesting performances to the 600+ subscribers in a future update.

Good luck!





 

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