How to sum up these fractions? Found this question in a competitive math test for elementary stude

herbariak1

herbariak1

Answered question

2022-05-24

How to sum up these fractions?
Found this question in a competitive math test for elementary students. The long way is to add all the decimal values but is there a pattern/trick to solve this question (or these types)? I don't know how to solve this except by the long method of adding all the decimal equivalents.
The Answer is 1
Compute:
1 7 + 1 8 + 1 9 + 1 10 + 1 11 + 1 12 + 1 14 + 1 15 + 1 18 + 1 22 + 1 24 + 1 28 + 1 33 = ?

Answer & Explanation

hoffwnbu

hoffwnbu

Beginner2022-05-25Added 13 answers

Not sure if this is what you are looking for but this is what I did:
S = 1 7 + 1 8 + 1 9 + 1 10 + 1 11 + 1 12 + 1 14 + 1 15 + 1 18 + 1 22 + 1 24 + 1 28 + 1 33
I observed the following groupings:
1. 7, 14, 28
2. 8, 12, 24
3. 11, 22, 334. I did grunt work on the remaining four numbers and found that the LCM is 90
S = 1 7 + 1 14 + 1 28 1 4 + 1 8 + 1 12 + 1 24 1 4 + 1 11 + 1 22 + 1 33 1 6 + 1 9 + 1 10 + 1 15 + 1 18 1 3
S = 1 4 + 1 4 + 1 6 + 1 3
= 1 2 + 1 2 = 1

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