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 number. - Multiplying or dividing two integers with different signs results in a negative number. - When multiplying or dividing multiple integers, count the number of negative factors: if even, the result is positive; if odd, the result is negative. 3. **Solve each multiplication problem:** (1) $(-6)(3)$ - Different signs, so result is negative. - Multiply absolute values: $6 \times 3 = 18$ - Result: $-18$ (2) $-8 \times (-5)$ - Same signs, so result is positive. - Multiply absolute values: $8 \times 5 = 40$ - Result: $40$ (3) $12 \cdot (-3)$ - Different signs, so result is negative. - Multiply absolute values: $12 \times 3 = 36$ - Result: $-36$ (4) $9(4)$ - Both positive, result positive. - Multiply: $9 \times 4 = 36$ - Result: $36$ (5) $(4)(-2)(3)$ - Count negatives: 1 (odd), so result negative. - Multiply absolute values: $4 \times 2 \times 3 = 24$ - Result: $-24$ (6) $(-3)(5)(-2)$ - Count negatives: 2 (even), so result positive. - Multiply absolute values: $3 \times 5 \times 2 = 30$ - Result: $30$ (7) $(1)(-6)(-7)(-1)(2)$ - Count negatives: 3 (odd), so result negative. - Multiply absolute values: $1 \times 6 \times 7 \times 1 \times 2 = 84$ - Result: $-84$ 4. **Solve each division problem:** (1) $8 \div (-2)$ - Different signs, result negative. - Divide absolute values: $8 \div 2 = 4$ - Result: $-4$ (2) $(-18) \div (-3)$ - Same signs, result positive. - Divide absolute values: $18 \div 3 = 6$ - Result: $6$ (3) $15 \div (-5)$ - Different signs, result negative. - Divide absolute values: $15 \div 5 = 3$ - Result: $-3$ (4) $-21 \div (-7)$ - Same signs, result positive. - Divide absolute values: $21 \div 7 = 3$ - Result: $3$ (5) $-54 \div 9$ - Different signs, result negative. - Divide absolute values: $54 \div 9 = 6$ - Result: $-6$ (6) $39 \div (-3)$ - Different signs, result negative. - Divide absolute values: $39 \div 3 = 13$ - Result: $-13$ (7) $-64 \div -8$ - Same signs, result positive. - Divide absolute values: $64 \div 8 = 8$ - Result: $8$