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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

  Yukio Kobayashi

  29-32

  15-06-2022

  Abstract Views: 140 PDF Download: 70

• PROOF WITHOUT WORDS: $a, b, c, d>0$; $ \frac{a}{b}=\frac{c}{d} \Rightarrow \frac{a}{b}=\frac{c}{d}=\frac{s a+t c}{s b+t d} $

  Yukio Kobayashi

  71-77

  07-08-2024

  Abstract Views: 250 PDF Download: 108