One Ninth

A Maths Starter Of The Day

One Ninth

Three fractions add together to give one ninth.

If all the question marks represent the same number, what is that number?

What if all the question marks represent different numbers?

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Topics: Starter | Fractions | Investigations

  • Inger Kisby, Herts and Essex High School
  • Wednesday, January 31, 2007
  • "The lemon law was wonderful as it catered for all abilities. My year 7 top set also enjoyed the fractions adding up to one ninth"
  • Harrytown Catholic High School, 9A
  • Friday, January 30, 2009
  • "We found the 1/27 + 1/27 + 1/27 quite easily, we then had a good discussion at the different denominators. We initially thought it was 1/26 + 1/27 + 1/28 but we did manage to prove this did not work. We eventually found the solution 1/18 + 1/27 + 1/54 using some algebra."
  • Grade 12 Advanced Functions, Port Hope, Ontario, Canada
  • Monday, January 18, 2010
  • "My class determined that one of the denominators had to be 9 and then the other two could be +2 and -2, or +3 and -3, or + 4 and -4, etc."
  • Lucius Evans, Mandeville
  • Wednesday, February 02, 2011
  • "My year 7 students cracked this up much faster than I anticipated. Thereafter they were led to write up their own following this pattern.Interestingly they increased the number of fractions and went beyond unit fractions."

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This starter has scored a mean of 3.4 out of 5 based on 88 votes.


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Answers

If all the question marks represent the same number there is only one answer:

One Ninth Answer 1

If all the question marks represent different numbers there are countless solutions. Here is one:

One Ninth Answer 2

See also the Starter called One Fifth.


Laptops In Lessons

Teacher, do your students have access to computers?
Do they have Laptops in Lessons or iPads?

Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Laptops In Lessons

Here is the URL for a concise version of this page without comments or answers.

Transum.org/go/?Start=January31

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

Transum.org/go/?to=Fractions

 

Show students how to create fractions in MS Word:

From the 'Insert' menu choose 'Object' then 'Microsoft Equation'

Microsoft Equation

It's even easier with "Math Input Panel" which comes with Windows 7.

 

Extension

Unique Fraction Sum

What is unique about this fraction sum?


Extension Answer

All the digits 0 to 9 are used.

It is the only way to use the digits 0 to 9 to make fractions adding up to one?



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