Question

escride la fraccion irreducible, equvalente a cada par de fraciones.

$a. \: \frac{78}{104} y \frac{45}{60}$
$b. \: \frac{21}{63} y \: \frac{32}{96}$
$c. \: \frac{86}{215} \: y \: \frac{60}{150}$
$d. \: \frac{54}{36} \: y \: \frac{63}{42}$





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Answer 1

Respuesta:

Explicación paso a paso:

Descompondremos cada fracción en factores y luego cancelaremos los factores comunes, quedando al final, una fracción irreductible, entonces:

$\frac{78}{104}\,\,\texttt{y}\,\,\frac{45}{60}\\\\\frac{78}{104}=\frac{(2)(39)}{(2)(52)}=\frac{(2)(3)(13)}{(2)(2)(26)}=\frac{(2)(3)(13)}{(2)(2)(2)(13)}=\frac{3}{(2)(2)}=\frac{3}{4}\\\\\frac{45}{60}=\frac{(9)(5)}{(2)(30)}=\frac{((3)(3)(5)}{(2)(6)(5)}=\frac{(3)(3)(5)}{(2)(2)(3)(5)}=\frac{3}{(2)(2)}=\frac{3}{4}$

$\frac{21}{63}\,\,\texttt{y}\,\,\frac{32}{96}\\\\\frac{21}{63}=\frac{(3)(7)}{(3)(21)}=\frac{(3)(7)}{(3)(3)(7)}=\frac{1}{3}\\\\\frac{32}{96}=\frac{(4)(8)}{(3)(32)}=\frac{((2)(2)(2)(4)}{(3)(4)(8)}=\frac{(2)(2)(2)(2)(2)}{(3)(2)(2)(2)(2)(2)}=\frac{1}{3}$

$\frac{86}{215}\,\,\texttt{y}\,\,\frac{60}{150}\\\\\frac{86}{215}=\frac{(2)(43)}{(5)(43)}=\frac{2}{5}\\\\\frac{60}{150}=\frac{(2)(30)}{(5)(30)}=\frac{2}{5}$

$\frac{54}{36}\,\,\texttt{y}\,\,\frac{63}{42}\\\\\frac{54}{36}=\frac{(6)(9)}{(6)(6)}=\frac{(2)(3)(3)(3)}{(2)(3)(2)(3)}=\frac{3}{2}\\\\\frac{63}{42}=\frac{(7)(9)}{(6)(7)}=\frac{(7)(3)(3)}{(2)(3)(7)}=\frac{3}{2}$

Saludos