Basic math concepts which you learn in algebra are the foundation for chemistry related problems. Order of operations, exponents, and graphing skills are all things which are absolutely necessary in more advanced science classes.
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Math will help, not hinder, you in this. You actually need a LOT of math, especially for physics and engineering.
Chemistry isn't entirely math. The math in chemistry isn't very complicated, it's just understand how to apply the math AND understand some of the key concepts.
For calculating specific amounts of medicine given to the patient. Doctors can pretty much double major in chemistry because of all they need to know on chemistry in general.
You can do Chemistry if you're interested in Chemistry and want to learn something about it. There's no connection between it and math, in either direction.
Not generally true. On the other hand, if you're bad at math you're going to have a TOUGH time with chemistry, and an even worse time with physics. Most of Chemistry and Physics IS math. You'll be fine.