Unit conversions:
Example: convert #("x centimeters")/("1 second") -> ("Kilometers")/("year")#
#(x cm)/(1 sec) * (1m)/(100cm) * (1Km)/(1000m) * (60sec)/(1min) * (60min)/("1 hour") * ("24 hour")/("1 day") *("365 day")/("1 year")#
#=(x*60*60*24*365 Km)/(100*"1000 year")#
Calculus:
Derivative calculation, second derivative calculation, using those to find the local maximum, local minimum, and points of inflection (example: titrations)
Algebraic equation manipulation:
Example: combined gas law
If #(P_1*V_1)/T_1=(P_2*V_2)/T_2# you could imagine that a certain piece were x to solve for it individually:
If #V_1=x#, then solving for x would look like #x=(P_2*V_2)/T_2 *(T_1)/(P_1)#
