Far East Journal of Mathematical Education

The Far East Journal of Mathematical Education is a peer-reviewed journal focused on mathematical education. It publishes research papers that enhance understanding of mathematical concepts and encourages the use of technology, statistics, algorithms, and simulations in mathematics learning.

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PROOF WITHOUT WORDS: $\frac{a}{b}=\frac{c}{d} \Rightarrow \frac{a}{b}=\frac{c}{d}=\frac{a \pm c}{b \pm d}$ IN THE RANGE OF NATURAL NUMBERS

Authors

  • Yukio Kobayashi

Keywords:

fractions, ratio.

DOI:

https://doi.org/10.17654/0973563122006

Abstract

To facilitate comprehension of the theorem $\frac{a}{b}=\frac{c}{d} \Rightarrow \frac{a}{b}=\frac{c}{d}=$ $\frac{a \pm c}{b \pm d}$ intuitively in the range of natural numbers at the elementary arithmetic level, a pictorial proof of this theorem is presented. The diagrams used for this proof can also help primary and secondary students understand the meaning of ratios or fractions.

Received: March 1, 2022 
Accepted: March 28, 2022

References

Yukio Kobayashi, Proof without words: componendo et dividendo, a theorem on proportions, College Math. J. 45 (2014), 115.

Richard A. Gibbs, Math. Mag. 63 (1990), 172.

Li Changming, Mathematics Teacher 81 (1988), 63.

Roger B. Nelsen, Math. Mag. 67 (1994), 34.

Roger B. Nelsen, Proofs without Words, The Mathematical Association of America, Washington, 1993.

Roger B. Nelsen, An invitation to proofs without words, European Journal of Pure and Applied Mathematics 3 (2010), 118-127.

Yukio Kobayashi, Visual thinking of mathematical concepts, Far East Journal of Mathematical Education 10(2) (2013), 157-174.

Sara Katz, Moshe Stupel and Ruth Segal, Proof without words with geometric representations: a trigger to self-efficacy and mathematical argumentation, Far East Journal of Mathematical Education 16(1) (2016), 21-56.

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Published

15-06-2022

Issue

Vol. 22 (2022)

Section

Articles

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How to Cite

PROOF WITHOUT WORDS: $\frac{a}{b}=\frac{c}{d} \Rightarrow \frac{a}{b}=\frac{c}{d}=\frac{a \pm c}{b \pm d}$ IN THE RANGE OF NATURAL NUMBERS. (2022). Far East Journal of Mathematical Education, 22, 29-32. https://doi.org/10.17654/0973563122006

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