# Obtaining Fractions via Folding Paper

- Author:
- Terry Tam

- Topic:
- Constructions, Fractions

Halves (1/2) can be simply found by folding a square paper. However, finding tri-sections (1/3 and its multiples) may not be trivial.
a) Using Haga's First Fold, drag point E (pretending corner B after folding) to point M (midpoint of the opposite side of AB) to see how tri-sections can be obtained. Could you explain why?
b) Using Haga's Third Fold, drag point E along the opposite side so that point J coincides with point N (midpoint of the opposite side of BC) to see another way to obtain tri-sections. Could you explain why?
c) Using Haga's First Fold, drag point E to quadrisection (1/4) of the opposite side of AB to see how to quintsect (5-sect) a line (and also its multiples). Do you find how to 7-sect? Could you generalize for other fractions as well?
d) As the result of part a), how 6-sections and 8-sections can be obtained?
e) As the result of part b), how 9-sections can be obtained? Do you find another way to get 6-sections as well?