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
Hi Murray,
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
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
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
Your nephew should now be able to complete the assignment.
Cheers |

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