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

Share

Topics: Starter | Arithmetic

• Vanessa Howe, howesvc@aol.com
•
• What is the answer to November 6ths starter of the day?
• Sarah, Newcastle
•
• Its 108/99. I used it today before i did "changing recurring decimals into fractions Y10 MOD 3.
• David Gee, Notting Hill Prep School
•
• 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
•
• 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
•
• Jacob Savage in year 7 from Swavesey Village college also noticed that these two numbers worked.....
9818181819 / 9000000000.
• Declan, Liverpool
•
• 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
•
• 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
•
• 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
•
• WOW What a starter- it took us ages to work it out!
• Vicky, Stoke Fleming
•
• Help- my class still haven't managed it? Help.

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.

If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:

Excellent, I would like to see more like this
Good, achieved the results I required
Satisfactory
Didn't really capture the interest of the students
Not for me! I wouldn't use this type of activity.

This starter has scored a mean of 3.0 out of 5 based on 545 votes.

Previous Day | This starter is for 6 November | Next Day

#### 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.

Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon search box and some items chosen and recommended by Transum Mathematics to get you started.

## Hello World

You are buying a (driverless) car. One vehicle is programmed to save as many lives as possible in a collision. Another promises to prioritize the lives of its passengers. Which do you choose?

Welcome to the age of the algorithm, the story of a not-too-distant future where machines rule supreme, making important decisions – in healthcare, transport, finance, security, what we watch, where we go even who we send to prison. So how much should we rely on them? What kind of future do we want?

Hannah Fry takes us on a tour of the good, the bad and the downright ugly of the algorithms that surround us. In Hello World she lifts the lid on their inner workings, demonstrates their power, exposes their limitations, and examines whether they really are an improvement on the humans they are replacing. more...

 Teacher, do your students have access to computers?Do they have iPads or Laptops in Lessons? Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Transum.org/go/?Start=November6

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

Transum.org/go/?to=Recurring

For Students:

For All: