Find the reciprocal of `3 (5)/(7)`.

Options

A. `7/26`
B. `26/7`
C. `7/25`
D. `25/7`

Answer

To find the reciprocal of \(3 \frac{5}{7}\), 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 \(3 \frac{5}{7}\) into an improper fraction, we multiply the whole number by the denominator and then add the numerator.

\[ 3 \frac{5}{7} = \frac{(3 \times 7) + 5}{7} = \frac{21 + 5}{7} = \frac{26}{7} \]

### Step 2: Find the reciprocal of the improper fraction.
The reciprocal of a fraction is obtained by swapping its numerator and denominator. Therefore, the reciprocal of \(\frac{26}{7}\) is:

\[ \text{Reciprocal} = \frac{7}{26} \]

### Step 3: Verify the result.
To ensure that \(\frac{7}{26}\) is indeed the reciprocal, we can multiply the original fraction by its reciprocal:

\[ \frac{26}{7} \times \frac{7}{26} = \frac{26 \times 7}{7 \times 26} = \frac{182}{182} = 1 \]

Since the product is \(1\), we have confirmed that \(\frac{7}{26}\) is the correct reciprocal.

### Final Answer:
The reciprocal of \(3 \frac{5}{7}\) is \(\frac{7}{26}\).

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