Jikjok calculated that the average number of flies eaten per minute by this gecko is

1.090909091

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

## A Mathematics Lesson Starter Of The Day

Topics: Starter | Arithmetic

• Vanessa Howe, howesvc@aol.com
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• What is the answer to November 6ths starter of the day?
• Sarah, Newcastle
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• Its 108/99. I used it today before i did "changing recurring decimals into fractions Y10 MOD 3.
• David Gee, Notting Hill Prep School
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• 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
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• 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
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• Jacob Savage in year 7 from Swavesey Village college also noticed that these two numbers worked.....
9818181819 / 9000000000.
• Declan, Liverpool
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• The solution is simply incorrect. The the average was exactly 1.090909091, then he would have 1090909091 in 1000000000. However, 1090909091 is prime and this fraction does not simplify. The answer is 1090909091 flies in 1000000000 minutes. The proposed solution: 12 flies in 11 minutes is incorrect because 12/11 ≠ 1.090909091. In fact 12/11 has an infinite decimal expansion of the form 1.090909090909090909090....
• 5/6A, SAHPS
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• We the students in 5/6A at SAHPS found this one challenging but we came up with an original solution. Yeah ! That was fun!
• P Rudd, Glan-y-Mor Comprehensive
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• The answer 12/11 is correct because it says using a standard calculator, which is why only the first 10 digits of the answer is shown. Great question as many younger students believe an answer containing so many decimal places must be wrong!
Thanks Transum.
• Benjamin Garrett, Watford
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• WOW What a starter- it took us ages to work it out!
• Vicky, Stoke Fleming
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• Help- my class still haven't managed it? Help.
• Larry, Math Teacher
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• 1.090909...is a recurring simple fraction so it would be 1 whole and 9/99 as you have 2 digits for the repeating period Then you simplify by 9 and get 1 whole and 1/11. When you convert the mixed into an improper fraction you get 12/11. That means 12 flies every 11 minutes. Hope that helps!

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#### Recurring Decimal

Use your calculator to find which whole number divided by another whole number gives the answer 1.36363636
This Starter also has a related pupil activity.

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 Teacher, do your students have access to computers such as tablets, iPads or Laptops?  This page was really designed for projection on a whiteboard but if you really want the students to have access to it here is a concise URL for a version of this page without the comments: Transum.org/go/?Start=November6 However it would be better to assign one of the student interactive activities below.

Here is the URL which will take them to a related student activity.

Transum.org/go/?to=Recurring

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