Find the reciprocal of: 3. `5(3)/(5)`

Answer

To find the reciprocal of the mixed fraction \(5 \frac{3}{5}\), we will follow these steps:

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

For \(5 \frac{3}{5}\):
- Whole number = 5
- Numerator = 3
- Denominator = 5

The calculation will be:
\[ 5 \times 5 + 3 = 25 + 3 = 28 \]
So, the improper fraction is:
\[ \frac{28}{5} \]

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

For the fraction \(\frac{28}{5}\):
- The numerator is 28
- The denominator is 5

The reciprocal will be:
\[ \frac{5}{28} \]

### Final Answer
The reciprocal of \(5 \frac{3}{5}\) is \(\frac{5}{28}\).

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