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Maths Item of the Month

September 2021

Unit fractions in the Sand Reckoner diagram

The Sand Reckoner diagram is created by joining the corners of a unit square to the midpoints of non-adjacent sides. 

Sand Reckoner diagram for September 2021 Maths Item of the Month

Show that in the diagram the blue lengths are all unit fractions:

$$AA’ = \dfrac{1}{2} \textrm{, }BB’=  \dfrac{1}{3} \textrm{, }CC’=  \dfrac{1}{4} \textrm{ and }DD’=  \dfrac{1}{5} $$

What other unit fractions can be found in the diagram?  

Looking for more problems?

Check out past editions in our resources listing.