Full equations in PDF document here drive.google.com/file/d/1OP3c...

Wow, and "persistent links" so "each time you press Save, the link will stay the same" 😍 Not sure why this and better file management took so terribly long to address, but I'll just be grateful it finally happened!

My solution to the puzzle: When does this flawed application of the zero-product property still yield correct solutions? www.dropbox.com/s/m8zyey3we4...

I believe misunderstanding of needing a zero, for my students at least. Or beyond “misunderstanding,” often no compulsion to understand why it works in the first place. Curious how that might vary across schools.

And this post elsewhere from user @potetoichiro

Wow, down another rabbit hole, and there are more of those than I thought! Along the way I saw another post attributing this one to James Tanton: 12345679/98765432 = 1/8

Great question for advanced students: Under what conditions does this flawed application of the zero-product property produce correct results? (Of course, ask with caution, at risk of creating more confusion🫠)

I wish I didn't have to ever see this again! Too often having to remind that the ZERO product property actually requires a zero on one side of equation. But at least here's one contrived case where the incorrect algebra yields a correct solution 😜

Same for hs→undergrad. Maybe Math teachers are more inclined to consider that only 1 in 20 are top 5%, but others may rank half their students as top 5%. And does my assessment of top 10% look unfavorable to another teacher's top 5%, even though our populations might be totally different?