Fresh Market is making 22 1/2 pounds of trail mix. 1/3 of the mix will be raisins, 1/5 of the mix will be M&M’s candy, and the remainder of the mix will be nuts. How many pounds of nuts are needed for the trail mix? Express the answer as a fraction in simplest form.
1/3 of the mix will be raisins, or (1/3)(22 1/2) = 22 1/2 / 3 = <<22.5/3=7 1/2>>7 1/2 pounds of raisins
1/5 of the mix will be M&M's candy, or (1/5)(22 1/2) = 22 1/2 / 5 = <<22.5/5=4 1/2>>4 1/2 pounds of M&M's candy
If the remaining amount of the mix will be nuts, then the amount of nuts is 22 1/2 - 7 1/2 - 4 1/2 = 22 1/2 - 12 = <<22.5-12=10 1/2>>10 1/2 pounds of nuts.
Fresh Market will need 10 1/2 pounds of nuts for the trail mix. Answer: \boxed{\frac{10}{2}}.