Intelligent Math Puzzle – Challenge 85

Challenge:

There are 4 fractions in the figure above with the same difference. What is the sum of all fractions?

A-(frac{1}{126})

B- (frac{7}{33})

C- (frac{13}{42})

D- (frac{10}{66})

E- (frac{13}{21})

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There are four fractions with the same difference. First, we need to find the missing fractions.
The difference of (frac{1}{7}) and (frac{1}{6}) is:
(frac{1}{6}, frac{1}{7}/7 = frac{7-6}{42} = frac{1}{42})
The difference of (frac{1}{7}) and the first fraction is:
(frac{1}{42} ÷3 = frac{1}{126})
The first missing fraction is:
(frac{1}{7} + frac{1}{126}= frac{18+1}{126} = frac{19}{126})
The second missing fraction is:
(frac{19}{126} + frac{1}{126}= frac{20}{126})
The sum of all fractions equals:
(frac{1}{7} + frac{19}{126}+ frac{20}{126} + frac{1}{6} = frac{18}{126}+ frac{19}{126} + frac{20}{126} + frac{21}{126} = frac{78}{126} = frac{13}{21})

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