Find the multiple inverse or reciprocal of each of the following :
(i) 18
(ii) -16
(iii) `(13)/(25)`
(iv) `(-17)/(12)`
(v) `(-6)/(19)`
(vi) `(-3)/(-5)`
(vii) -1
(viii) 0

Answer

To find the multiplicative inverse (or reciprocal) of each of the given numbers, we will follow these steps:

### Step-by-Step Solution:

**(i) For 18:**
- The multiplicative inverse of a number \( x \) is given by \( \frac{1}{x} \).
- Therefore, the multiplicative inverse of 18 is:
\[ \frac{1}{18} \]

**(ii) For -16:**
- The multiplicative inverse of -16 is:
\[ \frac{1}{-16} = -\frac{1}{16} \]

**(iii) For \( \frac{13}{25} \):**
- The multiplicative inverse of \( \frac{13}{25} \) is:
\[ \frac{25}{13} \]

**(iv) For \( \frac{-17}{12} \):**
- The multiplicative inverse of \( \frac{-17}{12} \) is:
\[ \frac{12}{-17} = -\frac{12}{17} \]

**(v) For \( \frac{-6}{19} \):**
- The multiplicative inverse of \( \frac{-6}{19} \) is:
\[ \frac{19}{-6} = -\frac{19}{6} \]

**(vi) For \( \frac{-3}{-5} \):**
- The multiplicative inverse of \( \frac{-3}{-5} \) is:
\[ \frac{-5}{-3} = \frac{5}{3} \]

**(vii) For -1:**
- The multiplicative inverse of -1 is:
\[ \frac{1}{-1} = -1 \]

**(viii) For 0:**
- The multiplicative inverse of 0 is undefined because you cannot divide by zero. In mathematical terms, we often say it is infinity.

### Summary of Answers:
1. \( \frac{1}{18} \)
2. \( -\frac{1}{16} \)
3. \( \frac{25}{13} \)
4. \( -\frac{12}{17} \)
5. \( -\frac{19}{6} \)
6. \( \frac{5}{3} \)
7. \( -1 \)
8. Undefined (or infinity)