Find the product in simplest form.

two-fifths × start fraction 3 over 7 end fraction
A. fourteen-fifteenths
B. Start fraction 5 over 12 End fraction
C. start fraction 6 over 35 end fraction
D. one-fifth

The product is:

two-fifths × start fraction 3 over 7 end fraction

= (2/5) x (3/7)

= 6/35

Therefore, the answer is C. Start fraction 6 over 35 end fraction.