1. **State the problem:** Multiply and divide the given integers using the Rules-Based Method. 2. **Rules for multiplication and division of integers:** - Multiplying or dividing two integers with the same sign results in a positive integer. - Multiplying or dividing two integers with different signs results in a negative integer. - The absolute values are multiplied or divided as usual. 3. **Solve each multiplication problem:** 1.) $(-6)(3) = -18$ because signs differ. 2.) $-8 \times (-5) = 40$ because signs are the same. 3.) $12 \cdot (-3) = -36$ because signs differ. 4.) $9(4) = 36$ both positive. 5.) $(4)(-2)(3) = (4 \times -2) \times 3 = -8 \times 3 = -24$. 6.) $(-3)(5)(-2) = (-3 \times 5) \times -2 = -15 \times -2 = 30$. 7.) $(1)(-6)(-7)(-1)(2)$ - First multiply first two: $1 \times -6 = -6$ - Then $-6 \times -7 = 42$ - Then $42 \times -1 = -42$ - Finally $-42 \times 2 = -84$ 4. **Solve each division problem:** 1.) $8 \div (-2) = -4$ signs differ. 2.) $(-18) \div (-3) = 6$ signs same. 3.) $15 \div (-5) = -3$ signs differ. 4.) $-21 \div (-7) = 3$ signs same. 5.) $-54 \div 9 = -6$ signs differ. 6.) $39 \div (-3) = -13$ signs differ. 7.) $-64 \div -8 = 8$ signs same. **Final answers:** Multiplication: $-18, 40, -36, 36, -24, 30, -84$ Division: $-4, 6, -3, 3, -6, -13, 8$