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Find the multiplicative inverse (i.e., reciprocal) of:

(i) \(\frac{13}{25}\)

(ii) \(\frac{-17}{12}\)

(iii) \(\frac{-7}{24}\)

(iv) 18

(v) -6

(vi) \(\frac{-3}{-5}\)

(vii) -1

(viii) \(\frac{0}{2}\)

(ix) \(\frac{2}{-5}\)

(x) \(\frac{-1}{8}\)

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A multiplicative inverse for a number x, is a number which when multiplied by x yields the multiplicative identity, 1 

The multiplicative inverse of a rational number is . \(\frac{a}{b}\) is \(\frac{b}{a}.\)

Therefore,

(i) The multiplicative inverse of \(\frac{13}{25}= \frac{25}{13}.\)

(ii) The multiplicative inverse of \(\frac{-17}{12}=\frac{12}{-17}.\)

In standard form,

\(\frac{12}{-17}=\frac{12\times-1}{-17\times-1}= \frac{12}{-17}.\)

(iii) The multiplicative inverse of \(\frac{-7}{24}=\frac{24}{-7}.\)

In standard form

\(\frac{24}{-7} = \frac{24 \times -1}{-4 \times -1} = \frac{-24}{7}\)

(iv) The multiplicative inverse of 18 = \(\frac{1}{18}.\)

(v) The multiplicative inverse of \(-6=\frac{1}{-6}.\)

\(\frac{1}{-6}=\frac{1\times-1}{-6\times-1}=\frac{-1}{6}\)

(vi) The multiplicative inverse of \(\frac{-3}{-5}=\frac{-5}{-3}.\)

In standard form,

\(\frac{-5}{-3}= \frac{-5\times-1}{-3\times-1}=\frac{3}{5}\)

(vii) The multiplicative inverse of -1 =-1.

(viii) The multiplicative inverse of \(\frac{0}{2}\)is undefined.

Since, \(\frac{2}{0}\)is undefined.

(ix) The multiplicative inverse of \(\frac{2}{-5}= \frac{-5}{2}.\)

(x) The multiplicative inverse of \(\frac{-1}{8}= \frac{8}{-1}.\)

In standard form,

\(\frac{8}{-1}= \frac{8\times-1}{-1\times-1}=\frac{-8}{1}=-8\)

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