High School A question about rules of multiplication

[logicgate]

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 ?

 

[symbolipoint]

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!


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small edit done

 

[DaveC426913]

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?

 

[FactChecker]

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.

 

[PeroK]

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 $y = z = 1$?