The Galactic Journey of Fractions

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Imagine you're on a space mission exploring a newly discovered galaxy, "Fractionus". This galaxy has 5 planets, each with unique environments. Your task is to gather data on these planets. On your journey:

  1. Planet Alpha: You collected 1/3 of the needed mineral samples.
  2. Planet Beta: You found another 1/4 of the samples.
  3. Planet Gamma: You gathered 1/6 of the total samples.
  4. Planet Delta: This time, you collected 1/8 of the samples.
  5. Planet Epsilon: The final planet, where you managed to collect 1/12 of the samples.

Your mission is to calculate the total fraction of mineral samples you collected from all five planets. Did you manage to collect more than half of the samples needed for your research?

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