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mtanti
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Why is it that when you do A * b/c the answer is one (b/c)th of A? What is the operation of multiplication doing to the two numbers so that this happens? Also how does this logic work when A is also a fraction?
Why is it that when you do A * b/c the answer is one (b/c)th of A?
1/3 of 4 is the same as 4 thirds, by commutativity of multiplication.mtanti said:Yes but why is it that you use multiplication to findthat (1/3)rd or 4? From what you say you are just showing that you are finding 4 thirds and not (1/3)rd of 4.
What is the difference?mtanti said:...you are finding 4 thirds and not (1/3)rd of 4.
mtanti said:I know how to multiply, but I seem to misunderstand what it does in practice to physical quantities. Why is it that when you multiply 2 apples by 1/2 you get 1/2 of 2 = 1 apple.
Does it really?eieio said:mtanti:
Look at it like this:
1 * A = A
I think it's clear this makes sense to you concretely.
arildno said:Does it really?
Why?
Does that string of symbols mean anything independently from definitions you set up?
I still think that my explanation in https://www.physicsforums.com/showpost.php?p=1083624&postcount=2" explains it.mtanti said:Why is it that to find a fraction of a quantity (say 1/2 of 100), you multiply that quantity by the fraction. What does multiplication have to do with finding fractions of quantities?
(For nonzero b) the definition of (a/b) is that it's the unique number such that:A * a/b = (A/b) * a
which means that you first break A into b equal pieces and then add the magnitude of 'a' of those pieces.
mtanti said:Guess I am just trying to understand fractions and their relationship to operators. Does it work that way because it is defined that way that a/b means multiply by a and divide by b or is there more to it?