I watched the 2nd video of Percentage, and I have a question.

Doesn’t ‘product’ mean ‘multiply’?

In the class, the question was ‘What percentage is 3 of 12?’
and Greg solves is like dividing.
3/12=1/4
1/4*100=25%.

I think 25% is correct, but I don’t know why ‘of’ is not multiplying.
In the other question, ‘What is 25% of 12?’, x=1/4x12, which ‘of’ was ‘multiply.’

Because it’s not the same question. 25% of 12 means 1/4 times (of) 12

But what percentage is 3 of 12 is an entirely different question asking for a different solution. Here you need to find 25 as the solution not 3. I hope that helps a little?

I discussed it with a math teacher, and he said that the question is wrong.
To have 25% as an answer, the question should have been ‘3 is what percent of 12?.’
I’m more confused now… could you please help to explain?

Hey, I think you are confused by the semantics mate. “3 is what percent of 12?” And “What percentage is 3 of 12?” is the same thing. Your teacher is correct that the answer will be 25%, but the question is not wrong.

I think you can skim through a couple of problems from the Manhattan 5lb book and I am confident you’ll get used to the kind of language they use

‘3 is what percent of 12?’ And ‘What percentage is 3 of 12?’ are the same questions?
I’m not a native speaker and so as my teacher.
He said that ‘What percentage is 3 of 12’ equation should be x=3 * 12 * 100, and ‘3 is what percent of 12?’ equation should be 3=x * 1/100 * 12, which I learned that ‘of’ should be represented as 'multiply.
Can you see why i’m confused here? I only thought that ‘of’ is ‘multiplying’ whatsoever. This thought is too binary to think?
Thank you for recommending the book, but I think if I just think ‘of’ is ‘multiplying’, things won’t be different. When I see the question, should I think ‘of’ can be proposition or multiplying?

Thank you for spending your time to read my questions and reply to me!

How about you rephrase the question in your head like the following to make it make sense to you like the following: “What percentage of 12 is 3?” I think this will help you tackle this kind of questions

You are very welcome and it’s a problem that both natives and non-natives face I believe, so don’t worry, you’ll be just fine!