1. **Problem Statement:** Determine which numbers from the list 38, 45, 76, 92, 288, 358, 876, 1580, 23, 494 are divisible by 4. 2. **Rule for divisibility by 4:** A number is divisible by 4 if the number formed by its last two digits is divisible by 4. 3. **Check each number:** - 38: last two digits 38; 38 ÷ 4 = 9.5 (not divisible) - 45: last two digits 45; 45 ÷ 4 = 11.25 (not divisible) - 76: last two digits 76; 76 ÷ 4 = 19 (divisible) - 92: last two digits 92; 92 ÷ 4 = 23 (divisible) - 288: last two digits 88; 88 ÷ 4 = 22 (divisible) - 358: last two digits 58; 58 ÷ 4 = 14.5 (not divisible) - 876: last two digits 76; 76 ÷ 4 = 19 (divisible) - 1580: last two digits 80; 80 ÷ 4 = 20 (divisible) - 23: last two digits 23; 23 ÷ 4 = 5.75 (not divisible) - 494: last two digits 94; 94 ÷ 4 = 23.5 (not divisible) 4. **Numbers divisible by 4:** 76, 92, 288, 876, 1580 5. **Answer for 6a:** Circle 76, 92, 288, 876, 1580. 6. **Problem 6b:** Is it correct to say a number is divisible by 4 if half of the number is even? 7. **Explanation:** - If half of a number is even, it means that when you divide the number by 2, the result is an even number. - An even number can be written as $2k$ for some integer $k$. - So, if half the number is even, the number can be written as $2 \times (2k) = 4k$. - This means the original number is a multiple of 4 and thus divisible by 4. 8. **Conclusion:** Yes, it is correct to say a number is divisible by 4 if half of the number is even because that implies the number is a multiple of 4.