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

(i) 9

(ii) -7

(iii) 12/5

(iv) -7/9

(v) -3/-5

(vi) 2/3 × 9/4

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

(viii) -2 × -3/5

(ix) -1

(x) 0/3

(xi) 1

1 Answer

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Best answer

(i) The reciprocal of 9 is 1/9

(ii) The reciprocal of -7 is -1/7

(iii) The reciprocal of 12/5 is 5/12

(iv) The reciprocal of -7/9 is 9/-7

(v) The reciprocal of -3/-5 is 5/3

(vi) The reciprocal of 2/3 × 9/4 is

\(\frac{2}{3}\times\frac{9}{4}\\=\frac{18}{12}\\=\frac{3}{2}\)

Hence ,the reciprocal is 2/3

(vii) The reciprocal of -5/8 × 16/15 is

\(\frac{-5}{8}\times\frac{16}{15}\\=\frac{-80}{120}\\=\frac{-2}{3}\)

Hence The reciprocal of -2/3 is 3/-2

(viii) The reciprocal of \(-2\times\frac{-3}{5}\) is

\(= \frac{6}{5}\)

∴ Hence ,The reciprocal of 6/5 is 5/6

(ix) The reciprocal of -1 is -1

(x) The reciprocal of 0/3 does not exist

(xi) The reciprocal of 1 is 1

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