Tim works at a hardware store has 8 1/2 pounds of nails to be sorted into bags. How many bags will Tim be able to fill if he puts 1/4 pounds of nails into each bag?

(8 1/2) / (1/4) = (17/2) * (4/1) = ?

To determine the number of bags Tim will be able to fill, we need to divide the total weight of the nails by the weight of each bag.

First, convert the mixed number 8 1/2 to an improper fraction. Multiply the whole number (8) by the denominator (2), which equals 16. Then, add the numerator (1) to get 17. So, 8 1/2 is equal to 17/2.

Next, divide the total weight of nails (17/2 pounds) by the weight of each bag (1/4 pounds).

To divide fractions, we need to remember that dividing is the same as multiplying by the reciprocal. So, we will multiply 17/2 by the reciprocal of 1/4, which is 4/1.

Now, multiply the numerator (17) of the first fraction by the numerator (4) of the second fraction to get 68. Then, multiply the denominator (2) of the first fraction by the denominator (1) of the second fraction to get 2.

So, 17/2 * 4/1 = 68/2 = 34.

Therefore, Tim will be able to fill 34 bags with the given amount of nails.