To multiply two fractions, we simply multiply their numerators together and their denominators together.
So, to find the product of 3/10 and 5/10, we have:
(3/10) x (5/10) = (3 x 5) / (10 x 10) = 15/100
Since 15 and 100 have a common factor of 5, we can simplify the fraction by dividing both the numerator and denominator by 5:
15/100 = (15 ÷ 5) / (100 ÷ 5) = 3/20
Therefore, the product of 3/10 and 5/10 is 3/20, which is a proper fraction.