The expression 30 ÷ 1/5 of 25 is resulting into 150 on Wolfram|Alpha.
I think 'of' and multiplication are little different.
Number on the left and number on the right of 'of' should be taken as if they are in bracket i.e.
30 ÷ (1/5 of 25). Although it can be seen in the picture that it is reading the input correctly, but still the result is showing as 150.
30 ÷ 1/5 of 25... Is that thirty divided-by one-fifth-of-twenty-five or is that thirty-divided-by-one-divided-by-five of 25?
When we speak we give pauses to help donate where the brackets go, and even then it can be ambiguous at times. I did get a different result using the Unicode for 1/5, but not the one you were hoping for: 30 ÷ ⅕ of 25 came out to 30/(1/5)×25
30 ÷ ⅕ of 25
I think your reasoning is reasonable. But, I can see it from the other side.
That is why you will see me use parenthesis more often than technically needed. Sometimes my reasonable reasoning is not reality.
Have a great rest of your week.
I love trying to figure out how to google interesting questions like this. But, I am not able to figure out how to google "precedence of of".
That said, I think reasonable people (and machines) can disagree on whether "of" and "multiplication" are the same or different.
Great question. It makes one think.
Thanks for replying Mike.
I think since 'of' conveys the meaning of 'some part of something' as in
'three fifth of fifty' or '25% of n',
it should be treated as a group and not as a common multiplication operation represented by X or *.