So first, I would convert 3/5 to 6/10, because it is equivalent and easier.
You can then just deduce that 1/10 would be 1/6 of 6/10, and that each person would therefore get 1/10 of a pound of peanuts.
You could also divide 3/5 by 6.
3/5 / 6 = 3/5 * 1/6
3/5 * 1/6 = 3/30
3/30 = 1/10