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)$\frac{0}{3}$

(ix)-1 (xi)1

Answer 1

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

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

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

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

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

(vi)Multiplicative inverse of$\frac{2}{3}\times \frac{9}{4}=\frac{3}{2}\times \frac{4}{9}=\frac{3\times 4}{2\times 9}=\frac{1\times 2}{1\times 3}=\frac{2}{3}$

(vii)Multiplicative inverse of $\frac{-5}{8}\times \frac{16}{15}=\frac{8}{-5}\times \frac{15}{16}=\frac{8\times 15}{-5\times 16}=\frac{1\times 3}{-1\times 2}=\frac{3}{-2}=\frac{3\times (-1)}{-2\times (-1)}=\frac{-3}{2}$

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

(ix)Multiplicative inverse of -1 = -1

(x)Multiplicative inverse of 0 = Does not exist as division by 0 is not admissible.

(xi)Multiplicative inverse of 1 = 1.