Tree Frog

A Maths Starter of The Day

Kermit calculated that the average number of flies eaten per minute by this tree frog is

1.090909091

He found this by dividing a whole number of flies by a whole number of minutes. What were those two whole numbers?

Calculators are allowed!

 

 

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Keywords: Starter | Arithmetic

  • Vanessa Howe, howesvc@aol.com
  • Monday, November 06, 2006
  • "What is the answer to November 6ths starter of the day?"
  • Sarah, Newcastle
  • Monday, November 06, 2006
  • "Its 108/99. I used it today before i did "changing recurring decimals into fractions Y10 MOD 3."
  • David Gee, Notting Hill Prep School
  • Friday, November 06, 2009
  • "The numbers are 12 divided by 11 (108/99 cancelled down). The clue is in the recurring decimal - a two digit cycle 090909... for 1/11 181818... for 2/11 272727... for 3/11 . Elevenths as decimals have two digit cycles of the multiples of nine."
  • David Gee, Notting Hill
  • Monday, November 09, 2009
  • "Sorry, typo in cut and paste! 1/11 is 0.090909 (1x9) 2/11 0.181818 (2x9)
    3/11 0.272727 (3x9)."
  • Jacob, Swavesey Village Collge
  • Tuesday, November 10, 2009
  • "Jacob Savage in year 7 from Swavesey Village college also noticed that these two numbers worked.....
    9818181819 / 9000000000."
  •  

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Answers

This problem can be solved by "trial and improvement" or as follows.

Let us assume that the calculator Kermit used has rounded of a recurring decimal. Let this number be x.

x = 1.090909....

100x = 109.090909.....

Subtract the first equation from the second

99x = 108

x = 108/99

x = 12/11

So the two numbers were 12 and 11 (or any multiples of them).

12 flies in 11 minutes!