Question

AYUDA EJERCICIOS CON FRACCIONES

Answer 1

Respuesta:

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Answer 2

Explicación paso a paso:

${(a - b)}^{2} = ({( 1\frac{1}{2} )}^{2} - {( \frac{1}{4} )}^{1} )^{2} \\ (a - b) ^{2} = ( { (\frac{3}{2}) }^{2} - \frac{1}{4})^{2} \\ {(a - b)}^{2} = ( \frac{9}{4} - \frac{1}{4} )^{2} \\ {(a - b)}^{2} = { (\frac{9}{4}) }^{2} - 2( \frac{9}{4} )( \frac{1}{4} ) + {( \frac{1}{4}) }^{2} \\ {(a - b)}^{2} = \frac{81}{4} - \frac{18}{4} + \frac{1}{16} \\ {(a - b)}^{2} = \frac{4(81) - 4(18) + 1}{16} \\ {(a - b)}^{2} = \frac{253}{16} \\ {(a - b)}^{2} = 15 \frac{13}{16}$

$d - b = {(1 \frac{2}{5} )}^{2} - {( \frac{1}{4}) }^{1} \\ d - b = (\frac{7}{5})^{2} - \frac{1}{4} \\ d - b = \frac{49}{25} - \frac{1}{4} \\ d - b = \frac{4(49) - 25(1)}{100} \\ d - b = \frac{196 - 25}{100} \\ d - b = \frac{171}{100} \\ d - b = 1 \frac{71}{100}$

$(c \times b)^{2} = ( (\frac{2}{3} )^{3} \times ( \frac{1}{4})^{1} )^{2} \\ {(c \times b)}^{2} = (( \frac{8}{27} )( \frac{1}{4} ))^{2} \\ {(c \times b)}^{2} = {( \frac{8}{108} )}^{2} \\ {(c \times b)}^{2} = \frac{64}{11664} \\ {(c \times b)}^{2} = \frac{4}{729}$

$\frac{c}{a} = \frac{ (\frac{ {2} }{3} )^{ 3} }{ {(1 \frac{1}{2}) }^{2} } \\ \frac{c}{a} = \frac{ \frac{8}{27} }{ {( \frac{3}{2}) }^{2} } \\ \frac{c}{a} = \frac{ \frac{8}{27} }{ \frac{9}{4} } \\ \frac{c}{a} = \frac{8 \times 4}{27 \times 9} \\ \frac{c}{a} = \frac{32}{243}$