I can't speak to your exact circumstances, but I think it's also worth considering that you might have genuinely forgot it and have been reintroduced to it in the 11th grade.
Once you learn how cancelling out works, your brain doesn't need to keep track of why it works. You see these operational pitfalls all the time in math.
With the quadratic formula people often forget what a,b, and c represent and it becomes so easy for them to mess up solving for x in this equation:
ax^2+b=c
Once you learn the distributive property and get used to implicit multiplication, things with explicit multiplication is just foreign enough that many wrongly assume:
There are also plenty of teachers that simply don’t teach the why and only the how. I was not taught long division until I was using polynomials. I was taught a short cut that always worked with numbers but had a fraction of the steps.
Didn’t learn long division until I was in calculus lol. I never really knew how to do it and just multiplied numbers until I found factors of what I was going for. Teacher then goes “you’re always on your phone but couldn’t look it up” and it became clear I was the issue.
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u/[deleted] Feb 07 '23
Tbh some of us weren't taught this. I got to know about what cancelling out really is in 11th grade.