Is Multiplication Really Just Repeated Addition?

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SUMMARY

The forum discussion centers on the debate surrounding the definition of multiplication, specifically whether it should be viewed as repeated addition. Participants argue that while multiplication can be seen as repeated addition in the context of natural numbers, this perspective fails to hold in higher mathematics, such as with matrices or real numbers. The consensus is that multiplication and addition are fundamentally different operations, and teaching them as such is crucial for a deeper understanding of mathematics. The discussion highlights the importance of distinguishing between these operations to avoid misconceptions in mathematical education.

PREREQUISITES
  • Understanding of basic arithmetic operations: addition, subtraction, multiplication, division.
  • Familiarity with the concept of inverse operations in mathematics.
  • Knowledge of higher mathematics concepts, including matrix multiplication and real numbers.
  • Basic understanding of mathematical pedagogy and teaching methods.
NEXT STEPS
  • Research the properties of multiplication in higher mathematics, focusing on matrix multiplication.
  • Explore the concept of bilinearity and its implications in algebra.
  • Study the differences between rational and real number operations, particularly in multiplication.
  • Investigate effective teaching strategies for introducing multiplication and addition to students.
USEFUL FOR

Mathematics educators, students in engineering or mathematics fields, and anyone interested in the foundational concepts of arithmetic and their implications in higher mathematics.

  • #91
The dole is always a counterexample to staying in school...
 
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  • #92
The dole is always a counterexample to staying in school...

That's pretty disrespectful of the young.

The average youth unemployment rate (through no fault of their own) currently stands at 25% and reaches over 50% in some areas.

Those who do get jobs do so, not on their academic record but by knowing the rich and powerful, if recent news articles are to be believed.

go well
 
  • #93
I think that multiplication is the unique operation which satisfies the distributive property, and, when applied to integers, is equivalent to repeated addition.
 
  • #94
epsi00 said:
try to multiply e by pi. e from exponential 1 and pi = 3.14...you'd see it's not a repeated addition at all.

I think it is...add e to itself 3 times, then add some more 'stuff'
 

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