I see two sections. Everything before the first space is the integral section. Everything after the first space is the fractional section. After you separate the two sections, you can just strip spaces from the fractional section, split that section on the / character, and divide the first part by the 2nd part (if there is a 2nd part). Then add the result to the integral section to find your answer.
This algorithm should give a correct result for each of your samples. It might also give an incorrect result for samples like these: "9 .25/4" or "9 3/0", so those are things to watch for. Other things include leading whitespace, whether you want to allow other whitespace, currency symbols, whether "9.25" (no spaces) is a valid input, and what to do with irrational fractions like "1/3", "1/10" (irrational in binary), etc.
I'm not normally a huge believer in test driven design (that you should write the tests first and go for 100% coverage) for static-typed languages, but I do think unit tests have value in certain specific situations, and this is one of those situations. I would put together a few tests for both some common and edge cases, such that you can be sure whatever you end up with handles the inputs correctly to pass the tests.