Sir, my nephew is having trouble with math,he is in grade 10. this is his question.

Find seven unit fractions whose whole sum is one.

thank you
murray

Hi Murray,
Unit fractions, fractions with the numerator one, are sometimes called Egyptian fractions. They seem to be the only fractions that appear on the ancient Egyptian wall paintings and papyrus scrolls.
  The easiest answer to your question is

1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 = 1

But I don't think that is what you are looking for. I think that you probably want to solve "Find seven different unit fractions whose whole sum is one".
  Lets look at a smaller problem. "Find three different unit fractions whose whole sum is one". Start with the largest unit fraction, 1/2, and add the next largest, 1/3. 1/2+1/3=5/6 which is one sixth less than 1 so

1/2 + 1/3 + 1/6 = 1

  Now try "Find four different unit fractions whose whole sum is one". Again start with 1/2 and 1/3 but 1/6 is now too large since it gets you a sum of 1 so try the largest unit fraction less than 1/6, that is 1/7. Adding you get 1/2+1/3+1/7=41/42 which is one forth-second less than 1 so

1/2 + 1/3 + 1/7 + 1/42 = 1

  Now five. Again start with 1/2, 1/3 and 1/7. 1/42 is too large so try 1/43. Then 1/2+1/3+1/7+1/43=1805/1806 which is 1/1806 less than 1 so

1/2 + 1/3 + 1/7 + 1/43 + 1/1806 = 1

Your nephew should now be able to complete the assignment.

Cheers
Penny

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