My take: Adding proportions is kinda "semantically incorrect". It's well defined as a value, it just doesn't mean what you think it means, akin to thinking that

My take: Adding proportions is kinda "semantically incorrect". It's well defined as a value, it just doesn't mean what you think it means, akin to thinking that union of two sets is written A + B (which would be the set of pair-wise additions of elements). Now, dovetailing the equation with units that signify concrete quantities (as suggested by others) circumvents this by making it meaningful, at the cost of no longer working with the abstract concept of proportion. An example of semantically meaningful manipulation of proportions is the weighted combination of proportions. This here's a more verbose version of what the teacher wrote: (3/6)* (1/3) + (3/6)*(1/3) = 1/3 (that is, the weighted average of the proportions give the final proportion)