Is it obvious that (a+c)/(b+d) is between a/b and c/d?

For positive whole numbers a, b, c and d. The result is called the mediant theorem, and I have seen it described as non-intuitive.

What if it is framed as follows? A team plays b games at the start of the season and wins a of them. Out of the remaining d games, it wins c. The winning rate for the whole season, (a+c)/(b+d), must be between the winning rate for the start of the season, a/b, and the wining rate for the end of the season, c/d.

Here is another sports application. Going into a game, a baseball player is batting .300. In the game, the player goes one for four, which must lower his average.