Question

Express -5/6 as a rational number with numerator;
i)-15
ii)10​

Answer 1

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i)

$in \: oder \: to \: express \: \frac{ - 5}{6} \: as \: a \: rational \: number \: with \: numerator \: - 15 \: we \: first \: find \: a \: number \: which \: when \: multiplied \: by \: - 5 \: gives \: - 5. \: clearly \: such \: number \: is \: ( - 15) + ( - 5) = 3$

$multiplying \: the \: numerator \: and \: the \: denominator \: of \: \frac{ - 5}{6} \: by \: 3 \: we \: have$

$\frac{ - 5}{6} = \frac{( - 5) \times 3}{6 \times 3} = \frac{ - 15}{18}$

$thus \: the \: required \: rational \: number \: is \: \frac{ - 15}{18}$

ii)

$in \: order \: to \: express \: \frac{ - 5}{6} \: as \: a \: ratonal \: number \: with \: numerator \: 10 \: we \: first \: find \: a \: number \: which \: when \: multiplied \: by \: - 5 \: gives \: 10.$

$clearly \: such \: a \: number \: is \: 10 \div ( - 5) = - 2.$

$multiplying \: the \: numerator \: and \: denominator \: of \: \frac{ - 5}{6} \: by \: ( - 2) \: we \: have \: \\ \frac{ - 5}{6} = \frac{( - 5) \times ( - 2)}{6 \times ( - 2)} = \frac{10}{ - 12}$

$thus \: the \: required \: rational \: number \: is \: \frac{10}{ - 12}$

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Answer 2

$\huge\rm{Answer:}$

1) $\to$ -15 / 18

2) $\to$ 10/ -12