To multiply signed numbers, we multiply the absolute values, and the sign of the product is determined by the rule that states:
- When multiplying two numbers with the same sign, the product's sign is positive.
- When multiplying two numbers with different signs, the product's sign is negative.
First, we multiply the absolute values of -2/5 and 3/10:
|-2/5| * |3/10| = (2/5) * (3/10) = 6/50
Since the signs are different (one negative and one positive), the product will be negative. Therefore, the answer is -6/50. However, we are asked to write the answer in simplest form.
To simplify the fraction, we divide the numerator and denominator by their greatest common divisor (GCD), which is 2 in this case.
-6/50 divided by 2/2 = (-6/2) * (1/25) = -3/25
Hence, the correct answer is -3/25.