question_answer

By what number should \[{{\left( -15 \right)}^{-1}}\] be divided so that the quotient is\[{{\left( -15 \right)}^{-1}}\].

Answer:

Let the number \[{{\left( 15 \right)}^{1}}\] should be divided by x to get the quotient\[{{\left( 5 \right)}^{1}}\]. \[\therefore {{(15)}^{1}}\div x={{(5)}^{1}}\] \[\frac{1}{-15}\div x=\frac{1}{-5}\] \[\frac{1}{-15}\times \frac{1}{x}=\frac{1}{-5}\] \[\frac{1}{-15x}=\frac{1}{-5}\] 15x × 1 = ? 5 × 1                                                                                                               15x = ? 5 \[x=\frac{-5}{-15}\] \[x=\frac{-1}{-3}\]