What is the largest possible value for the sum of two fractions such that each of the four 1 digit prime numbers occurs as one of the numerators or denominators?

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- May 28th 2007, 08:46 AMGodfatherNumerators and Denominators
What is the largest possible value for the sum of two fractions such that each of the four 1 digit prime numbers occurs as one of the numerators or denominators?

- May 28th 2007, 09:23 AMSoroban
Hello, Godfather!

Quote:

What is the largest possible value for the sum of two fractions such that

each of {2, 3, 5, 7} occurs as one of the numerators or denominators?

The sum of two fractions is: .

For the largest value, we want the*smallest denominator.*

. . This occurs for: . .(or vice versa).

We have: .

Then we have two choices: .

If

If

Therefore: . .is the largest sum.