Gen Chem maths

For dimensional analysis, you want to think in terms of what you have and what you want. You need to cancel out what you have and you *don't* want to cancel out what you want. For everything other than what you want, you need to have one unit in the top (numerator) and one unit in the bottom (denominator). Doing this will cause all the units that you don't want to cancel out, leaving you with the units you want.

So if I wanted to convert 5 cups of liquid to X Tablespoons of liquid, you start with cups: 5 cups (now you need to convert cups into something else, so you need cups in the denominator so the cups cancels out) so, (5 cups/ 1) * (8 fl oz / 1 cup). Now you need fl oz in the denominator to cancel out the fl oz you introduced in the second part of the calculation, so (5 cups/1) * (8 fl oz/ 1 cup) * (2 tablespoons / 1 fl oz). Now you multiply the numerators together and divide by all the denominators, and cancel out units which you have one in the numerator and one in the denominator, so 5/1*8/1*2/1 = 80, now for the units (cups/cups) gets rid of cups, (fl oz/ fl oz) gets rid of fl oz. So all you have left is tablespoons.

Remember, anything divided by itself is 1. (chickens)/(chickens) = 1 (farts)/(farts)= 1 (grams)/(grams)=1

This is how canceling units works.

Thank you that was very helpful!! Your last example made me laugh :) I will practice some problems over the weekend