1. **Problem:** There are 4 different Mathematics books and 5 different Filipino books. In how many ways can the books be arranged on a shelf if books of the same subject must be placed together? 2. **Formula and Explanation:** When books of the same subject must be together, treat each subject group as a single item first, then arrange the books within each group. - Number of ways to arrange the two groups (Mathematics and Filipino) = $2!$ - Number of ways to arrange 4 Mathematics books = $4!$ - Number of ways to arrange 5 Filipino books = $5!$ 3. **Calculation:** $$\text{Total ways} = 2! \times 4! \times 5!$$ $$= 2 \times 24 \times 120$$ $$= 2 \times 2880 = 5760$$ 4. **Answer:** The books can be arranged in **5760** ways if books of the same subject must be placed together.