1. **Problem:** Calculate $5256 \div 24$. 2. **Formula:** Division is the process of finding how many times the divisor fits into the dividend. Here, we want to find $\frac{5256}{24}$. 3. **Step-by-step calculation:** - Divide 5256 by 24. - First, estimate: $24 \times 200 = 4800$, which is less than 5256. - Try $24 \times 210 = 5040$, still less than 5256. - Try $24 \times 219 = 5256$ exactly. 4. **Verification:** $$24 \times 219 = 5256$$ 5. **Answer:** $$5256 \div 24 = 219$$ --- 6. **Problem:** Identify which expressions match the tape diagram: $x\quad x\quad x\quad 6\quad x\quad x\quad x\quad 6$. 7. **Understanding the tape diagram:** - The tape shows two groups: each group has $x + x + x + 6 = 3x + 6$. - Since there are two such groups, the total expression is $2(3x + 6)$. 8. **Check each option:** a) $2(x + x + x + 6) = 2(3x + 6)$ — matches the tape. b) $3x + 6$ — only one group, not the whole tape. c) $6x + 12$ — equivalent to $2(3x + 6)$ after distribution, matches. d) $2(3x + 6)$ — matches the tape. e) $6x - 12$ — subtraction, does not match. f) $x + x + x + 6 + x + x + x + 6 = 6x + 12$ — matches the tape. 9. **Final selections:** a), c), d), f).