- #1

Haris045

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- TL;DR Summary
- What is the link between proportion and multiplication? WHY DOES and how can multiplication model proportionality?

I found this quote online:

“Multiplication is the mathematical manifestation of the fundamental physical phenomenon of proportionality (as addition is to combination).”

Question 1: How are multiplication and proportion linked? How can and WHY DOES multiplication model proportion? (My understanding of proportion is the equivalence of ratios)

Also saw this "Multiplication is scaling a number up proportionally up or down"

Question 2: What does this mean to scale something up proportionally , proportionally to WHAT? . e.g. if I had 7.2 * 3.2 , how do I think of that as proportionally scaling? What am I scaling proportionally to what?

Edit:

These questions were formed when I was doing re-search on the true nature of multiplication, some things I have read about this topic:

https://www.maa.org/external_archive/devlin/devlin_06_08.html and https://www.maa.org/external_archive/devlin/devlin_01_11.html

I have also tried to read " Development of Multiplicative Reasoning in the Learning of Mathematics" it talked about multiplicative conceptual fields but it got quite confusing and dragged on and I didn't really understand the book.

Thanks in advance for the help!

“Multiplication is the mathematical manifestation of the fundamental physical phenomenon of proportionality (as addition is to combination).”

Question 1: How are multiplication and proportion linked? How can and WHY DOES multiplication model proportion? (My understanding of proportion is the equivalence of ratios)

Also saw this "Multiplication is scaling a number up proportionally up or down"

Question 2: What does this mean to scale something up proportionally , proportionally to WHAT? . e.g. if I had 7.2 * 3.2 , how do I think of that as proportionally scaling? What am I scaling proportionally to what?

Edit:

These questions were formed when I was doing re-search on the true nature of multiplication, some things I have read about this topic:

https://www.maa.org/external_archive/devlin/devlin_06_08.html and https://www.maa.org/external_archive/devlin/devlin_01_11.html

I have also tried to read " Development of Multiplicative Reasoning in the Learning of Mathematics" it talked about multiplicative conceptual fields but it got quite confusing and dragged on and I didn't really understand the book.

Thanks in advance for the help!