Question

✍️✍️solve this question...
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Answer 1

By what number should ${ - 30}^{ - 1}$ be divided to get ${6}^{ - 1}$ ?

❁ $\pink{\huge{ \rm{\underline{\underline{Solution }}}}}$ ❁

Let the number be x

Now, ${ - 30}^{ - 1}$ should be divided by x to get ${6}^{ - 1}$

We know that :-

❍ ${ - 30}^{ - 1} = \frac{ - 1}{30}$

❍ ${6}^{ - 1} = \frac{1}{6}$

As per the problem, we have:

$\frac{ (\frac{ - 1}{30} )}{x} = \frac{1}{6}$

◕ $\frac{( - \frac { 1}{30} )}{ \frac{1}{6} } = x$

◕ $x = - \frac{1}{30} \times \frac{6}{1} \: \: ( \because \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} )$

◕ $x = - {\frac{6}{30} } = - \frac{1}{5}$

Therefore,

$\green{ \underline{ \boxed{ \gray{ x = - \frac{1}{5} }}}}$

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$\blue{ \rm{</u></strong><strong><u>Let's</u></strong><strong><u> \: verify \: it</u></strong><strong><u> </u></strong><strong><u>:</u></strong><strong><u>-</u></strong><strong><u>}}$

We know,

${ (- 30)}^{ - 1}$ should be divided $- \frac{1}{5}$ to get ${6}^{ - 1}$

According to the problem, we have:

$\frac{ ({ - 30})^{ - 1} }{ - \frac{1}{5} }$

◉ $</u></strong><strong><u>=</u></strong><strong><u> </u></strong><strong><u>\frac{ - \frac{1}{30} }{ - \frac{1}{5} }$

Minus ( - ) sign will get cancel,

◉ $\frac{1}{30} \times \frac{5}{1} = \frac{5}{30}$

◉ $= \frac{1}{6}$

$\green{ \underline{ \boxed{ \gray{ {6}^{ - 1}}}}}$

Hence, Verified!!

$\blue{ \rm{Transposition :-}}$

A term may be transposed from one side of the equation to the other side, but its sign will change, i.e., plus ( + ) sign will become minus ( - ) and vica versa. Similarly, multiplication ( × ) sign changes into division ( ÷ ) sign and vice versa.

Applying all algebraic rules, we bring the linear variable in one side and other numerical terms or expressions to the other side of the equation. Then, make the coefficient of the variable 1 (unit).

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Answer 2

Givenu:-

• Quotient after dividing (- 30)^-1 with the unknown number = 6^-1

To Findu: The unknown number.

Let the unknown number be = $x$

According to the Question:-

${-30}^{-1} ÷ x = {6}^{-1}$

$\implies - \frac{1}{30} × \frac{1}{x} = \frac{1}{6}$

(We gave a numerator 1 to the numbers having - 1 as exponent becausu x^-1 = 1/x)

$\implies - \frac{1}{30x} = \frac{1}{6}$

By cross multiplying,

$\implies - 30x = 6$

$\implies - x = \frac{6}{30}$

$\implies -x = \frac{1}{5}$

$\implies x = - \frac{1}{5}$

$\implies x ={ - 5}^{-1}$

Hence, the required number is - 5^-1!

Hope it helps, Ms Sofia! :D

Regards,

@Spammore