To write the fraction 3 and 2/5 in its lowest terms, we need to simplify it.
First, we convert the mixed number 3 and 2/5 into an improper fraction.
To do this, we multiply the whole number (3) by the denominator (5), and then add the numerator (2). This gives us:
(3 * 5) + 2 = 15 + 2 = 17
Now, we write the improper fraction: 17/5.
To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator (17) and the denominator (5).
The factors of 17 are 1 and 17, while the factors of 5 are 1 and 5. Therefore, the only common factor is 1.
Since 1 is the only common factor, we can't simplify the fraction any further.
Hence, 3 and 2/5 in its lowest terms is already 17/5.