Step-by-Step Explanation:

Multiplying the Whole Number and the Mixed Fraction:
To multiply 3 by 5 1/5, we first need to convert the mixed fraction into an improper fraction. To do this, we multiply the whole number (5) by the denominator (5) and add the numerator (1) to get the new numerator for the improper fraction. So, 5 × 5 + 1 = 26. This gives us the improper fraction 26/5.

Multiplying the Whole Number by the Improper Fraction:
Next, we multiply the whole number (3) by the numerator of the improper fraction (26) to get the new numerator. 3 × 26 = 78. This becomes the numerator of our final answer.

Expressing the Result as a Mixed Fraction:
Now, we express the result as a mixed fraction. The denominator remains the same, which is 5. To convert the numerator (78) into a mixed number, we divide 78 by 5. 78 ÷ 5 = 15 with a remainder of 3.
Therefore, the final answer is 15 3/5. This means that 3 multiplied by 5 1/5 is equal to 15 3/5.