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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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 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:

However it would be better to assign one of the student interactive activities below.

Laptops In Lessons

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

Student Activity





Unique Fraction Sum

What is unique about this fraction sum?


One third of my family understand fractions while the other three quarters do not. I wonder which half of the family I am in!


Extension Answer


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