Difficulty with Word Problem

[Guest]

Please help with how to solve this problem.

In a chess tournament, 3/7 of the women are matched against half of the men. What fraction of all the players is matched against someone of the other gender?

The answer says it should be 6/13, but I do not know how they arrived at the answer.

Thanks for your help!

[Guest]

3 out of every 7 women are matched with men. (3 men pair 3 women)
and 4 out of every 7 women are matched with women. (2 women pair 2 women)
3 men is half the men so 3 more men making 6 men in the combined group of 7 women and 6 men. The 3 extra men can only make 1 pair of 2 men and 1 single man.
In chess need even number of pairs so double the size of the group.
That gives .....
6 men pair 6 women = 12 players
4 women pair 4 women = 8 players
3 men pair 3 men = 6 players

Total players all paired = 26
Total players pairing other gender = 12
Fraction pairing other gender = 12 / 26 = 6 /13

[Guest]

Thank you!!