1. Problem 1: Multiply and divide the following negative numbers. a) Calculate $-3 \times 4$. b) Calculate $12 \div (-3)$. Explanation: When multiplying or dividing numbers with different signs, the answer is negative. When signs are the same, the answer is positive. 2. Problem 2: Find the L.C.M and H.C.F of 12 and 18. Explanation: To find L.C.M, list multiples of each number until a common multiple is found. Multiples of 12: 12, 24, 36, 48... Multiples of 18: 18, 36, 54, 72... Common multiples: 36, 72... So L.C.M is 36. To find H.C.F, list factors of each number. Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 18: 1, 2, 3, 6, 9, 18 Common factors: 1, 2, 3, 6 So H.C.F is 6. 3. Problem 3: Critical thinking: If multiplying two numbers results in a positive number, what can you say about the signs of the two numbers? Explain. Explanation: Either both numbers are positive or both are negative, because multiplying numbers with the same signs results in a positive product. 4. Problem 4: Real-life question: A submarine is descending into the ocean at a rate of 5 meters per minute. After 10 minutes, how far below the surface is it? (Use negative numbers for depth.) Explanation: Depth after 10 minutes = $-5 \times 10 = -50$ meters below the surface. These problems review negative number multiplication and division, L.C.M and H.C.F, critical thinking on signs in multiplication, and a real-life application of negative numbers.