One Ninth

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?

A Mathematics Lesson Starter Of The Day


Topics: Starter | Fractions | Investigations

  • Inger Kisby, Herts and Essex High School
  • 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
  • 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
  • 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
  • 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.
  • Transum,
  • Thanks so much for sharing your solutions, methods and thoughts on this question. It is good to know that as your pupils are working on this task, students in other classrooms around the world are contemplating the very same conundrum. Reading others' comments helps bring the mathematics to life and create a sense of a community of learners enjoying this fascinating subject. Keep those comments, observations and anecdotes coming!

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Previous Day | This starter is for 31 January | Next Day



See also the Starter called One Fifth and a related GCSE question.

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Laptops In Lessons

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).

Laptops In Lessons

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

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

Student Activity


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.

In Word 2013 you can find the equation editor in the Insert tab.

Equation in Word




Unique Fraction Sum

What is unique about this fraction sum?



Extension Answer


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