`#3107.101107`
`4*5 = 2*10`
\(\Rightarrow\dfrac{4}{10}=\dfrac{2}{5}\\ \dfrac{5}{10}=\dfrac{2}{4}\\ \dfrac{10}{5}=\dfrac{4}{2}\\ \dfrac{10}{4}=\dfrac{5}{2}\)
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`6*63 = 9*42`
\(\Rightarrow\dfrac{6}{42}=\dfrac{9}{63}\\ \dfrac{63}{42}=\dfrac{9}{6}\\ \dfrac{63}{9}=\dfrac{42}{6}\\ \dfrac{6}{9}=\dfrac{42}{63}\)
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`14*15 = 10*21`
\(\Rightarrow\dfrac{14}{21}=\dfrac{10}{15}\\ \dfrac{21}{14}=\dfrac{15}{10}\\ \dfrac{10}{14}=\dfrac{15}{21}\\ \dfrac{14}{10}=\dfrac{21}{15}\)
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`ab = cd`
\(\Rightarrow\dfrac{a}{d}=\dfrac{c}{b}\\ \dfrac{d}{a}=\dfrac{b}{c}\\ \dfrac{c}{a}=\dfrac{b}{d}\\ \dfrac{a}{c}=\dfrac{d}{b}\)
\(4.5=2.10\Rightarrow\left\{{}\begin{matrix}\dfrac{4}{2}=\dfrac{10}{5}\\\dfrac{4}{10}=\dfrac{2}{5}\end{matrix}\right.\)
\(6.63=9.42\Rightarrow\left\{{}\begin{matrix}\dfrac{6}{9}=\dfrac{42}{63}\\\dfrac{6}{42}=\dfrac{9}{63}\end{matrix}\right.\)
\(14.15=10.21\)\(\Rightarrow\left\{{}\begin{matrix}\dfrac{14}{10}=\dfrac{21}{15}\\\dfrac{14}{21}=\dfrac{10}{15}\end{matrix}\right.\)
\(ab=cd\Rightarrow\left\{{}\begin{matrix}\dfrac{a}{c}=\dfrac{d}{b}\\\dfrac{a}{d}=\dfrac{c}{b}\end{matrix}\right.\)
