Find the reciprocal of : d. `4 (5)/(8)`

Answer

To find the reciprocal of the mixed number \(4 \frac{5}{8}\), we will follow these steps:

### Step 1: Convert the mixed number to an improper fraction.
A mixed number consists of a whole number and a fraction. To convert it to an improper fraction, we multiply the whole number by the denominator and add the numerator.

For \(4 \frac{5}{8}\):
- Whole number = 4
- Numerator = 5
- Denominator = 8

So, we calculate:
\[ 4 \times 8 + 5 = 32 + 5 = 37 \]
Thus, \(4 \frac{5}{8}\) can be written as:
\[ \frac{37}{8} \]

### Step 2: Find the reciprocal of the improper fraction.
The reciprocal of a fraction is obtained by swapping the numerator and the denominator.

For \(\frac{37}{8}\), the reciprocal is:
\[ \frac{8}{37} \]

### Final Answer:
The reciprocal of \(4 \frac{5}{8}\) is \(\frac{8}{37}\).

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