Find the reciprocal of each of the following fractions :
(i) `9/13" (ii) " 2""3/8`

Answer

To find the reciprocal of the given fractions, we will follow these steps:

### Step 1: Find the reciprocal of the first fraction \( \frac{9}{13} \)

1. The reciprocal of a fraction is obtained by swapping its numerator and denominator.
2. For the fraction \( \frac{9}{13} \), the numerator is 9 and the denominator is 13.
3. Therefore, the reciprocal is \( \frac{13}{9} \).

### Step 2: Find the reciprocal of the second fraction \( 2 \frac{3}{8} \)

1. First, we need to convert the mixed number \( 2 \frac{3}{8} \) into an improper fraction.
2. To convert a mixed number to an improper fraction, we multiply the whole number (2) by the denominator (8) and then add the numerator (3).
- Calculation: \( 2 \times 8 + 3 = 16 + 3 = 19 \)
3. So, \( 2 \frac{3}{8} \) can be written as \( \frac{19}{8} \).
4. Now, we find the reciprocal of \( \frac{19}{8} \) by swapping the numerator and denominator.
5. Therefore, the reciprocal is \( \frac{8}{19} \).

### Final Answers:
1. The reciprocal of \( \frac{9}{13} \) is \( \frac{13}{9} \).
2. The reciprocal of \( 2 \frac{3}{8} \) is \( \frac{8}{19} \).

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