Logics: If I need to find the number of apples in 500 3-apple boxes, why do I multiply?

Ryan$

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Hi guys, maybe it's so simply but I don't know why I find it hard!
if I want to calculate the number of apples in 500 vessel which every vessel is having 3 apples, so why the number of apples is 500*3? or actually why it's multiply? thanks alot
 

Ryan$

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when I exactly multiply ?
 

HallsofIvy

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What do you understand multiplication to mean?
 

Ryan$

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HallsofIvy

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Oh, dear! "Doubling" specifically means "multiplying by 2"! More generally, if you have 'm' boxes, each box containing 'n' things, then you have a total of m times n things. If you have things set out on the table in 'm' rows, each row of 'n' things then there are m times n things on the table (you can think of a "row" as a "box"). If a rectangle with width a cm and length b cm then its area is a times b "square centimeters" (you can think of the centimeters along the width as "rows" and the centimeter on the length as "things" in that row).
 

ksdhart2

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So you're saying that multiplication, always and forever, no matter what two numbers are being multiplied, means "doubled?" If that were true, if multiplication means "something to be doubled," then we have a huge difficulty because multiplication is an operation that involves two numbers. So which of those two is the "something" that's being doubled? If it's the first number, then we'd have the case that 2 * 5 means the same thing as 2 * 1 means the same thing as 2 * 17, and they all mean that two is being doubled. But how can that possibly be? Each of those expressions has definite, known values, and they're all different! Similarly, if it means the second number is being doubled, we'd have to admit that 3 * 4 means the same thing as 2 * 4 means the same thing as 16 * 4. And, again, each of those has definite, known values, and they're all different.

Instead, let's return to the very basics and figure out what's really going on here and see if we can't suss out what multiplication is. We're willing to accept, for the moment, that multiplication is the desired operation to figure out the total number of apples in 3 vessels of 500 apples each, but why is that the case? Can you see that if you had 2 vessels of 2 apples each and you put them all in one pile, you'd have 2 + 2 = 4 apples in total? Why is that? How did you know? Now suppose you had 3 vessels of 2 apples each. Can you see that if you put them all in one pile, you'd have 2 + 2 + 2 = 6 apples in total? Why is that? Are you seeing a pattern here? What if you had 4 vessels of 3 apples? And what if you had 5 vessels of 6 apples?

To sum up, we've seen that figuring out how many total apples are in your vessels is an application for repeated addition. And we've stated that multiplication also models this same idea. So, what does that tell you about how multiplication relates to repeated addition?

As an aside, "doubling" only refers to a specific type of multiplication, wherein one of the numbers is 2. For instance, we could say that 3 * 2 means 3 doubled, and 2 * 4 means 4 doubled.
 

Denis

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