To find the reciprocal of the mixed number \( 7 \frac{2}{5} \), follow these steps:
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Convert the mixed number to an improper fraction.
- First, multiply the whole number (7) by the denominator (5): \( 7 \times 5 = 35 \).
- Then, add the numerator (2) to this product: \( 35 + 2 = 37 \).
- So, \( 7 \frac{2}{5} \) can be written as \( \frac{37}{5} \).
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The reciprocal of a fraction is obtained by flipping the numerator and the denominator. Therefore, the reciprocal of \( \frac{37}{5} \) is \( \frac{5}{37} \).
Thus, the reciprocal of \( 7 \frac{2}{5} \) is \( \frac{5}{37} \).