Question

By what rational number should we multiply p/q so that the product is r/s ? (a) p/a = -2/11, r/s=6/11 (b) p/q +-12/13 , r/s =16/39

Answer 1

$\bf \underline{ \underline{\maltese\:Assumption } }$

$\sf Let \: the \: second \: rational \: number \: be \: x.$

$\bf \underline{ Now, }$

$\sf (a) \: \dfrac{ -2}{11} \times x = \dfrac{6}{11}$

$\sf \implies x = { \dfrac{ 6}{11} \times \dfrac{ - 11}{2} }$

$\sf \implies x = \dfrac{ -6}{2} = - 3$

$\sf Hence, \dfrac{ -2}{11} \: should \: be \: multiplied \: by \: - 3 \: to \: get \: \dfrac{6}{11}$

$\bf \underline{ Verification }$

$\sf \implies { \dfrac{ -2}{11} \times - 3} = \dfrac{6}{11}$

$\sf \implies \dfrac{6}{11} = \dfrac{6}{11}$

$\sf \implies LHS = RHS$

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$\sf (b) \: \dfrac{ -12}{13} \times x = \dfrac{16}{39}$

$\sf \implies x = { \dfrac{16}{39} \times\dfrac{ - 13}{12} }$

$\sf \implies x = { \dfrac{4}{3} \times\dfrac{ - 1}{3} } = \dfrac{ - 4}{9}$

$\sf Hence, \dfrac{ -12}{13} \: should \: be \: multiplied \: by \: \dfrac{ - 4}{9} \: to \: get \: \dfrac{16}{39}$

$\bf \underline{ Verification }$

$\sf \implies \dfrac{ -12}{13} \times \dfrac{ - 4}{9} = \dfrac{16}{39}$

$\sf \implies \dfrac{16}{39} = \dfrac{16}{39}$

$\sf \implies LHS = RHS$