Question

What should be added to
$\frac{ - 25}{27} to \: get \frac{ - 53}{54}$
​

Answer 1

$\\ \mathcal{ \huge \: \underline{ \underline{Question }}\: : }$

$\\ \sf \: What \: \: should \: \: be \: \: added \: \: to \: \: \frac{ - 25}{ \: \: 27} \: \: to \: \: get \: \: \frac{ - 53}{ \: \: \: 54} \: \: \large?$

$\\ \bf{ \huge \: \underline{ \underline{Answer}}\: : }$

$\\ \sf \: Let ~~the ~~number~~ to~~ be~~ added~~ be~~ x .$

$\\ \sf \frac{ - 25}{ \: \: \: 27} + x = \frac{ - 53}{ \: \: \: 54}$

$\\ \sf \: Taking \: \: \frac{ - 25}{ \: \: \: 27} \: \: to \: \: the \: \: RHS \: , \: where \: \: it \: \: will \: \: be \: \: added .$

$\sf \: x = \frac{ - 53}{ \: \: \: 54} + \frac{25}{ 27}$

$\sf \: LCM \: = \: 54$

$\sf \: x = \frac{ - 53}{ \: \: \: 54} + \frac{25 \times 2}{ 27 \times 2} \\ \\ \sf \: x = \frac{ - 53}{ \: \: \: 54} + \frac{50}{ 54} \\ \\ \sf \: x = \frac{ - 53 + 50}{54} \\ \\ \sf \: x = \frac{ - 3}{54} \\ \\ \underline{\underline{\sf x = \frac{ - 1}{18} }}$

$\\ \\ \boxed{ \tt \frac{ - 1}{ \: \: 18} \: \: should \: \: be \: \: added \: \: to \: \: \: \frac{ - 25}{ \: \: \: 27} \: \: to \: \: get \: \: \frac{ - 53}{ \: \: 54} }$

$\\ \\ \\ \bf \: Hope \: \: this \: \: helps \: \: you \: !$