Editing Openai/68a11068-3fe8-8007-bd18-674462ff2b41 (section)

=== Assistant: Great question 👌 and this gets right to the heart of the confusion. ===
Great question 👌 and this gets right to the heart of the confusion.

===== - It has a clear numerator and denominator. =====
* The whole denominator is just πr2\pi r^2πr2.
* No one could reasonably read it as πr2πr2\frac{\pi r^2}{\pi}r^2ππr2r2.

So:

πr2πr2=1(r≠0).\frac{\pi r^2}{\pi r^2} = 1 \quad (r \neq 0).πr2πr2=1(r=0).

===== Here the problem is: you’ve written division followed immediately by implicit multiplication. That creates two possible parses: =====
# Left-to-right (calculator / programming rule): (50/2)(1+4)=25⋅5=125(50/2)(1+4) = 25 \cdot 5 = 125(50/2)(1+4)=25⋅5=125
# Implicit multiplication “stronger than division” (algebra classroom rule): 50/(2(1+4))=50/10=550 / (2(1+4)) = 50 / 10 = 550/(2(1+4))=50/10=5

Both interpretations are common, depending on the convention.

===== - In πr2/πr2\pi r^2 / \pi r^2πr2/πr2, the denominator is just one unit: πr2\pi r^2πr2. No extra ambiguity. =====
* In 50/2(1+4)50/2(1+4)50/2(1+4), the denominator might be just 2 (if you go left-to-right), or the whole 2(1+4)2(1+4)2(1+4) (if you treat implicit multiplication as binding tighter).

✅ Rule of thumb:
* Fractions written with a horizontal bar (///) + implicit multiplication = ambiguous.
* Fractions written with a stacked fraction bar (……\frac{…}{…}……) = unambiguous.

Would you like me to make a side-by-side table of examples showing which are ambiguous vs unambiguous? That way you’ll see exactly where the traps are.