Find the multiplicative inverse (reciprocal) of each of the following rational numbers:
Question:

Find the multiplicative inverse (reciprocal) of each of the following rational numbers:

(i) 9

(ii) −7

(iii) $\frac{12}{5}$

(iv) $\frac{-7}{9}$

(v) $\frac{-3}{-5}$

(vi) $\frac{2}{3} \times \frac{9}{4}$

(vii) $\frac{-5}{8} \times \frac{16}{15}$

(viii) $-2 \times \frac{-3}{5}$

(ix) $-1$

(x) $\frac{0}{3}$

(xi) 1

Solution:

(i) Multiplicative inverse (reciprocal) of $9=\frac{1}{9}$

(ii) Multiplicative inverse (reciprocal) of $-7=\frac{-1}{7}$

(iii) Multiplicative inverse (reciprocal) of $\frac{12}{5}=\frac{5}{12}$

(iv) Multiplicative inverse (reciprocal) of $\frac{-7}{9}=\frac{-9}{7}$

(v) Multiplicative inverse (reciprocal) of $\frac{-3}{-5}=\frac{-5}{-3}$ or $\frac{5}{3}$

(vi) Multiplicative inverse (reciprocal) of $\frac{2}{3} \times \frac{9}{4}=\frac{3}{2} \times \frac{4}{9}=\frac{2}{3}$

(vii) Multiplicative inverse (reciprocal) of $\frac{-5}{8} \times \frac{16}{15}=\frac{8}{-5} \times \frac{15}{16}=\frac{-3}{2}$

(viii) Multiplicative inverse (reciprocal) of $-2 \times \frac{-3}{5}=\frac{1}{-2} \times \frac{5}{-3}=\frac{5}{6}$

(ix) Multiplicative inverse (reciprocal) of $-1=\frac{1}{-1}=-1$

$(\mathrm{x})$ Multiplicative inverse (reciprocal) of $\frac{0}{3}=\frac{3}{0}=$ undefined

(ix) Multiplicative inverse (reciprocal) of $1=\frac{1}{1}=1$