Find the multiplicative inverse (i.e., reciprocal) of :
`{:((i) (13)/(25), (ii) (-17)/(12) , (iii) (-7)/(24), (iv) 18, (v) -16),((vi) (-3)/(-5) , (vii) -1, (viii) (0)/(2), (ix) (2)/(-5), (x) (-1)/(8)):}`

Answer

To find the multiplicative inverse (reciprocal) of the given rational numbers, we will follow the rule that states: the multiplicative inverse of a fraction \( \frac{a}{b} \) is \( \frac{b}{a} \). For whole numbers, we can express them as fractions by placing them over 1.

Let's solve each part step by step:

### Step 1: Find the multiplicative inverse of \( \frac{13}{25} \)
- The reciprocal is obtained by swapping the numerator and denominator.
- So, the multiplicative inverse of \( \frac{13}{25} \) is \( \frac{25}{13} \).

### Step 2: Find the multiplicative inverse of \( \frac{-17}{12} \)
- Again, swap the numerator and denominator.
- The multiplicative inverse of \( \frac{-17}{12} \) is \( \frac{12}{-17} \) or simply \( -\frac{12}{17} \).

### Step 3: Find the multiplicative inverse of \( \frac{-7}{24} \)
- Swap the numerator and denominator.
- The multiplicative inverse of \( \frac{-7}{24} \) is \( \frac{24}{-7} \) or \( -\frac{24}{7} \).

### Step 4: Find the multiplicative inverse of \( 18 \)
- Express \( 18 \) as \( \frac{18}{1} \).
- The multiplicative inverse of \( 18 \) is \( \frac{1}{18} \).

### Step 5: Find the multiplicative inverse of \( -16 \)
- Express \( -16 \) as \( \frac{-16}{1} \).
- The multiplicative inverse of \( -16 \) is \( \frac{1}{-16} \) or simply \( -\frac{1}{16} \).

### Step 6: Find the multiplicative inverse of \( \frac{-3}{-5} \)
- The negatives cancel out, so this simplifies to \( \frac{3}{5} \).
- The multiplicative inverse of \( \frac{3}{5} \) is \( \frac{5}{3} \).

### Step 7: Find the multiplicative inverse of \( -1 \)
- Express \( -1 \) as \( \frac{-1}{1} \).
- The multiplicative inverse of \( -1 \) is \( \frac{1}{-1} \) or simply \( -1 \).

### Step 8: Find the multiplicative inverse of \( \frac{0}{2} \)
- The fraction \( \frac{0}{2} \) equals \( 0 \).
- The multiplicative inverse of \( 0 \) is undefined, as no number multiplied by \( 0 \) gives \( 1 \).

### Step 9: Find the multiplicative inverse of \( \frac{2}{-5} \)
- Swap the numerator and denominator.
- The multiplicative inverse of \( \frac{2}{-5} \) is \( \frac{-5}{2} \).

### Step 10: Find the multiplicative inverse of \( \frac{-1}{8} \)
- Swap the numerator and denominator.
- The multiplicative inverse of \( \frac{-1}{8} \) is \( \frac{8}{-1} \) or simply \( -8 \).

### Summary of Results:
1. \( \frac{13}{25} \) → \( \frac{25}{13} \)
2. \( \frac{-17}{12} \) → \( -\frac{12}{17} \)
3. \( \frac{-7}{24} \) → \( -\frac{24}{7} \)
4. \( 18 \) → \( \frac{1}{18} \)
5. \( -16 \) → \( -\frac{1}{16} \)
6. \( \frac{-3}{-5} \) → \( \frac{5}{3} \)
7. \( -1 \) → \( -1 \)
8. \( \frac{0}{2} \) → Undefined
9. \( \frac{2}{-5} \) → \( \frac{-5}{2} \)
10. \( \frac{-1}{8} \) → \( -8 \)