The problem provided is:

Melissa volunteers to make cookies for her 7th grade math class. Each batch of cookies requires 1 2/3 cups of flour. If she has twelve cups of flour, how many batches of cookies can she make?

Solution:

We need to determine how many times 1 2/3 cups of flour fits into 12 cups of flour.

1. First, convert the mixed fraction $1 \frac{2}{3}$ into an improper fraction: $1 \frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3}$

2. Now, divide the total flour (12 cups) by the amount of flour per batch $\frac{5}{3}$: $12 \div \frac{5}{3} = 12 \times \frac{3}{5} = \frac{36}{5} = 7.2$

So, Melissa can make 7 full batches of cookies, with some flour left over (about 0.2 of a batch).

Would you like more details on any part of the solution?

Here are 5 follow-up questions to expand on this topic:

1. How much flour will Melissa have left after making 7 batches?
2. If Melissa had 15 cups of flour, how many batches could she make?
3. What if each batch required 2 cups of flour instead of $1 \frac{2}{3}$? How many batches could she make with 12 cups?
4. How many cups of flour would Melissa need to make exactly 10 batches of cookies?
5. How many batches could she make if she had 20 cups of flour?

Tip: When dividing fractions, remember to multiply by the reciprocal of the second fraction!