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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


Answer :

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 \(-1=\frac{1}{-1}=-1 \qquad \)[∵ \(-1 ×\frac{1}{-1}=1\)]