Question

Write the multiplicative inverse of the following:

(1) $\frac{13}{4}$
(2) $\frac{4}{13}$
(3) $\frac{-3}{8}$
(4) $\frac{-8}{3}$
(5) $\frac{-16}{7}$
(6) $\frac{7}{6}$
(7) 5
(8) −2
(9) 1
(10) 11

Answer 1

If the multiplication of two numbers produces 1, then the two numbers are called reciprocal or multiplicative inverse of each other.
(1) $\frac{13}{4}$
The multiplicative inverse of $\frac{13}{4}\mathrm{is}\frac{4}{13}$ .

(2) $\frac{4}{13}$
The multiplicative inverse of $\frac{4}{13}\mathrm{is}\frac{13}{4}$ .

(3) $\frac{-3}{8}$
The multiplicative inverse of $\frac{-3}{8}\mathrm{is}\frac{8}{-3}=\frac{-8}{3}$ .

(4) $\frac{-8}{3}$
The multiplicative inverse of $\frac{-8}{3}\mathrm{is}\frac{3}{-8}=\frac{-3}{8}$ .

(5) $\frac{-16}{7}$
The multiplicative inverse of $\frac{-16}{7}\mathrm{is}\frac{7}{-16}=\frac{-7}{16}$ .

(6) $\frac{7}{6}$
The multiplicative inverse of $\frac{7}{6}\mathrm{is}\frac{6}{7}$ .

(7) 5
The multiplicative inverse of 5 is$\frac{1}{5}$ .

(8) −2
The multiplicative inverse of −2 is $\frac{1}{-2}=\frac{-1}{2}$ .

(9) 1
The multiplicative inverse of 1 is$\frac{1}{1}=1$ .

(10) 11
The multiplicative inverse of 11 is $\frac{1}{11}$ .