Math, asked by Anonymous, 10 months ago

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Answered by Mihir1001

$\huge{\underline{\mathfrak{\textcolor{blue}{Answer :}}}}$

$\huge\boxed{\fcolorbox{red}{pink}{41/35}}$

$\huge{\underline{\mathrm{\textcolor{red}{Step-by-step \: \: explanation :}}}}$

$\LARGE{\underline{\mathtt{\textcolor{violet}{Given :-}}}}$

product of two rational numbers $=$ $\large{ - \frac{12}{35} }$

one of the rational number $=$ $\large{ \frac{3}{5} }$

$\LARGE{\underline{\mathtt{\textcolor{green}{To \: \: find :-}}}}$

absolute value of the difference of the two rational numbers .

$\LARGE{\underline{\mathtt{\textcolor{teal}{Concept \: \: used :-}}}}$

Real Numbers

$\LARGE{\underline{\mathtt{\textcolor{blue}{Solution :-}}}}$

let the other rational number be x.

$\therefore \: ,$ A/Q,

$\longmapsto$ $\Large{ \frac{3}{5} \times x = - \frac{12}{35} }$

$\implies$ $\Large{ x = - \frac{12}{35} \times \frac{5}{3} }$

$\implies$ $\Large{ x = - \frac{ {}^{4} \: \cancel{12} }{_7 \: \cancel{35} } \times \frac{ \cancel{5} \: {}^{1} }{ \cancel{3} _1 } }$

$\implies$ $\Large{ x = - \frac{4}{7} }$

Hence, $\bold{ \frac{3}{5} }$ and $\bold{ - \frac{4}{7} }$ are the two rational numbers.

Thus,

absolute value of the difference of these rational numbers

$=$ $\Large{ | \frac{3}{5} - \left( - \frac{4}{7} \right) | }$

$=$ $\Large{ | \frac{3}{5} + \frac{4}{7} | }$

$=$ $\Large{ | \frac{(3)(7) + (4)(5)}{(5)(7)} | }$

$=$ $\Large{ | \frac{21 + 20}{35} | }$

$=$ $\Large{ | \frac{41}{35} | }$

$=$ $\Large{ \frac{41}{35} }$

$\LARGE{\underline{\mathtt{\textcolor{magenta}{Conclusion :-}}}}$

absolute value of the required difference $=$ $\Large{ \left( \frac{41}{35} \right) }$ $=$ $\Large{ \left( 1 \frac{6}{35} \right) }$

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