Find the reciprocal of
3`1/3`

Answer

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

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

Here, the whole number is 3, the numerator is 1, and the denominator is 3.

\[ 3 \frac{1}{3} = \frac{(3 \times 3) + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3} \]

**Step 2: Find the reciprocal of the improper fraction.**

The reciprocal of a fraction is obtained by flipping the numerator and the denominator. So, the reciprocal of \( \frac{10}{3} \) is:

\[ \text{Reciprocal} = \frac{3}{10} \]

**Final Answer:**

The reciprocal of \( 3 \frac{1}{3} \) is \( \frac{3}{10} \).

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