B A question about rules of multiplication

AI Thread Summary
Multiplication follows specific rules that prevent infinite distribution, unlike addition. When multiplying a number by a product, such as x times yz, the operation is defined to yield xyz rather than xyxz. Attempting to distribute multiplication in this way leads to an endless cycle of multiplication, which is not mathematically valid. Simple examples, like multiplying 3 by 7 times 8, illustrate that the result is consistently 3 times 7 times 8, equating to 168. Understanding these principles helps clarify the structure of multiplication in mathematics.
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Why is it that x times yz equals xyz and not xyxz ?
This might sound like a stupid question but I am just wondering why is it that x times yz equals xyz and not xyxz ? Why don't we distribute multiplication in this case ?
 
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Think back to the simplest meaning or way to understand Multiplication. Maybe try a known numbers simple example.

Why is it that 3 times 7*8 equals 3*7*8 and is not 3*7*3*8 ?

You can first show 7+7+7+7+7+7+7+7 and find that this is 56.
(Same thing can be expressed as 8+8+8+8+8+8+8.)

You can now show 3*56 to be 56+56+56 (excuse me if I not stayed in the same form.) And what is this resulting number value? 168.


You can also choose to show that example graphically or visually.

That should help!


---
small edit done
 
Here is multiplication in real life:

  1. I lay down 8 blocks in a row.
  2. I want to multiply that by 7, so I copy step 1 six more times, making a total of 7 columns of 8-block rows.
  3. I want to multiply that by 3, so I copy step 1 and 2 twice more, making the 7x8 matrix a total of 3 times, stacked.

Why would I multiply by 3 again?
 
logicgate said:
TL;DR Summary: Why is it that x times yz equals xyz and not xyxz ?

This might sound like a stupid question but I am just wondering why is it that x times yz equals xyz and not xyxz ? Why don't we distribute multiplication in this case ?
Trying to "distribute" multiplication over multiplication would never stop. It is not like distributing multiplication over addition.
If x times yz = xyxz, then why stop there? Wouldn't x distribute again to give xyxxxz? And again to give xyxxxxxxxz? etc. And there should be similar distribution from the right by z. So now we could say that xyxxxxxxxz = xzyzxzxzxzxzxzxzxz, and that could be done again ad infinitum.
 
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logicgate said:
TL;DR Summary: Why is it that x times yz equals xyz and not xyxz ?

This might sound like a stupid question but I am just wondering why is it that x times yz equals xyz and not xyxz ? Why don't we distribute multiplication in this case ?
Even if ##y = z = 1##?
 
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