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