A question about rules of multiplication

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Discussion Overview

The discussion revolves around the rules of multiplication, specifically addressing why the expression x times yz equals xyz rather than xyxz. Participants explore the conceptual understanding of multiplication and its application in various contexts.

Discussion Character

  • Conceptual clarification
  • Exploratory
  • Debate/contested

Main Points Raised

  • One participant questions why x times yz equals xyz and not xyxz, expressing confusion about the distribution of multiplication.
  • Another participant suggests using simple numerical examples to illustrate the concept, proposing that 3 times 7*8 equals 3*7*8 and not 3*7*3*8.
  • A participant describes a real-life scenario involving blocks to visualize multiplication, questioning the rationale behind multiplying by 3 again.
  • One participant argues that attempting to distribute multiplication over multiplication would lead to an infinite process, suggesting that such distribution is not analogous to distributing multiplication over addition.
  • A later post reiterates the initial question, even posing a hypothetical where y and z equal 1, to further explore the concept.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and confusion regarding the rules of multiplication. There is no consensus on a definitive explanation, and multiple viewpoints remain regarding the nature of multiplication and distribution.

Contextual Notes

Some participants rely on specific examples and visualizations, while others highlight the potential for confusion in the rules of multiplication. The discussion does not resolve the underlying assumptions or definitions related to multiplication.

logicgate
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TL;DR
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?
 
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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 ?
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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Likes   Reactions: renormalize and phinds

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