Fractions · Grades 5–8 · Unsolved

Erdős–Straus Conjecture

Any fraction with 4 on top can be split into three fractions with 1 on top.

Four fifths of a bar, rebuilt from a half, a fourth, and a twentieth. Same length exactly.

Try it

4/5 = 1/2 + 1/4 + 1/204/7 = 1/2 + 1/15 + 1/210

Ancient Egyptians wrote fractions this way almost 4,000 years ago.

Computers have checked it for more numbers than there are grains of sand on Earth.

Try 4/9. What’s your first move?

If you can split 4/5, can you split 4/10 for free?

Detailed one-pager (PDF) History, why it’s unsolved, and more classroom ideas