過去のtwitterのつぶやきより引用。
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(命題1:分数の掛け算)
b/a×d/c＝(b×d)/(a×c)
[証]
b/a×d/c＝(b×c)/(a×c)×d/c＝(b×c×d/c)/(a×c)＝(b×c×(1/c×d))/(a×c)
＝(b×(c×1/c)×d)/(a×c)＝(b×1×d)/(a×c)＝(b×d)/(a×c)■
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(命題2:分数の割り算)
b/a÷d/c=b/a×c/d
[証]
b/a÷d/c=b/a×1÷d/c=b/a×((c×d)/(c×d))÷d/c=b/a×((c×d)/(d×c))÷d/c
=b/a×(c/d×d/c)÷d/c=b/a×c/d×(d/c÷d/c)=b/a×c/d×1=b/a×c/d■
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