# Find the multiplicative inverse (i.e., reciprocal) of: (i) 13/25 (ii) -17/12 (iii) -7/24 (iv) 18

1.1k views

closed

Find the multiplicative inverse (i.e., reciprocal) of:

(i) $\frac{13}{25}$

(ii) $\frac{-17}{12}$

(iii) $\frac{-7}{24}$

(iv) 18

(v) -6

(vi) $\frac{-3}{-5}$

(vii) -1

(viii) $\frac{0}{2}$

(ix) $\frac{2}{-5}$

(x) $\frac{-1}{8}$

+1 vote
by (26.1k points)
selected by

A multiplicative inverse for a number x, is a number which when multiplied by x yields the multiplicative identity, 1

The multiplicative inverse of a rational number is . $\frac{a}{b}$ is $\frac{b}{a}.$

Therefore,

(i) The multiplicative inverse of $\frac{13}{25}= \frac{25}{13}.$

(ii) The multiplicative inverse of $\frac{-17}{12}=\frac{12}{-17}.$

In standard form,

$\frac{12}{-17}=\frac{12\times-1}{-17\times-1}= \frac{12}{-17}.$

(iii) The multiplicative inverse of $\frac{-7}{24}=\frac{24}{-7}.$

In standard form

$\frac{24}{-7} = \frac{24 \times -1}{-4 \times -1} = \frac{-24}{7}$

(iv) The multiplicative inverse of 18 = $\frac{1}{18}.$

(v) The multiplicative inverse of $-6=\frac{1}{-6}.$

$\frac{1}{-6}=\frac{1\times-1}{-6\times-1}=\frac{-1}{6}$

(vi) The multiplicative inverse of $\frac{-3}{-5}=\frac{-5}{-3}.$

In standard form,

$\frac{-5}{-3}= \frac{-5\times-1}{-3\times-1}=\frac{3}{5}$

(vii) The multiplicative inverse of -1 =-1.

(viii) The multiplicative inverse of $\frac{0}{2}$is undefined.

Since, $\frac{2}{0}$is undefined.

(ix) The multiplicative inverse of $\frac{2}{-5}= \frac{-5}{2}.$

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

In standard form,

$\frac{8}{-1}= \frac{8\times-1}{-1\times-1}=\frac{-8}{1}=-8$