4.Find the multiplicative inverse of the following :
(i)-13

(ii)$$\frac{-13}{19}$$

(iii)$$\frac{1}5$$

(iv)$$\frac{-5}8×\frac{-3}{7}$$

(v)$$-1×\frac{-2}5$$

(vi)-1

We know that multiplicative inverse of a is $$\frac{1}a \qquad$$[∵ $$a ×\frac{1}a=1$$]

(i) Multiplicative inverse of $$-13=\frac{-1}{13} \qquad$$[∵ $$-13 ×\frac{-1}{13}=1$$]

(ii) Multiplicative inverse of $$\frac{-13}{19}=\frac{-19}{13} \qquad$$[∵ $$\frac{-13}{19} ×\frac{-19}{13}=1$$]

(iii) Multiplicative inverse of $$\frac{1}{5}=5 \qquad$$[∵ $$\frac{1}{5} ×5=1$$]

(iv) Multiplicative inverse of $$\frac{-5}8×\frac{-3}{7}=\frac{-8}5×\frac{-7}{3}$$

we have $$\frac{-5}8×\frac{-3}{7}=\frac{15}{56}$$

and we have the multiplicative inverse as $$\frac{-8}5×\frac{-7}{3}=\frac{56}{15}$$

∴ $$\frac{15}{56} ×\frac{56}{15}=1$$

(v) We have $$-1\frac{-2}5=\frac{2}5$$

∴Multiplicative inverse of $$\frac{2}5=\frac{5}2 \qquad$$[∵ $$\frac{2}{5} ×\frac{5}{2}=1$$]

(vi)Multiplicative inverse of $$-1=\frac{1}{-1}=-1 \qquad$$[∵ $$-1 ×\frac{1}{-1}=1$$]