Reciprocal of `1 3/5`

Options

A. `5/8`
B. `5 1/3`
C. `3 1/5`
D. `2 5/3`

Answer

To find the reciprocal of \(1 \frac{3}{5}\), we can 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 \(1 \frac{3}{5}\) to an improper fraction, we can use the formula:

\[ \text{Improper Fraction} = \left(\text{Whole Number} \times \text{Denominator} + \text{Numerator}\right) / \text{Denominator} \]

For \(1 \frac{3}{5}\):
- Whole Number = 1
- Numerator = 3
- Denominator = 5

Now, substituting these values into the formula:

\[ \text{Improper Fraction} = \left(1 \times 5 + 3\right) / 5 = \left(5 + 3\right) / 5 = 8 / 5 \]

### 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 \( \frac{8}{5} \):
- Numerator = 8
- Denominator = 5

Now, we swap them:

\[ \text{Reciprocal} = \frac{5}{8} \]

### Final Answer:
The reciprocal of \(1 \frac{3}{5}\) is \(\frac{5}{8}\).

---