Multiplying & Dividing Integers — Solutions

1. Sign Rule Identification

   1. (−4) × 3: Negative ▶ View Solution
   2. (−5) × (−2): Positive ▶ View Solution
   3. 7 × (−3): Negative ▶ View Solution
   4. (−8) ÷ (−4): Positive ▶ View Solution
   5. 12 ÷ (−3): Negative ▶ View Solution
   6. (−10) ÷ 5: Negative ▶ View Solution
   7. (−6) × (−6): Positive ▶ View Solution
   8. (−1) × 100: Negative ▶ View Solution

2. Multiplying Integers

   1. (−3) × 5: −15 ▶ View Solution
   2. 4 × (−7): −28 ▶ View Solution
   3. (−6) × (−4): 24 ▶ View Solution
   4. (−9) × 3: −27 ▶ View Solution
   5. 8 × (−5): −40 ▶ View Solution
   6. (−7) × (−7): 49 ▶ View Solution
   7. (−2) × 11: −22 ▶ View Solution
   8. (−10) × (−6): 60 ▶ View Solution

3. Dividing Integers

   1. (−12) ÷ 4: −3 ▶ View Solution
   2. 20 ÷ (−5): −4 ▶ View Solution
   3. (−18) ÷ (−3): 6 ▶ View Solution
   4. (−24) ÷ 6: −4 ▶ View Solution
   5. 36 ÷ (−9): −4 ▶ View Solution
   6. (−45) ÷ (−9): 5 ▶ View Solution
   7. (−32) ÷ 8: −4 ▶ View Solution
   8. (−56) ÷ (−7): 8 ▶ View Solution

4. Powers of Negative Numbers

   1. (−2)²: 4 ▶ View Solution
   2. (−2)³: −8 ▶ View Solution
   3. (−3)²: 9 ▶ View Solution
   4. (−1)⁵: −1 ▶ View Solution
   5. (−4)²: 16 ▶ View Solution
   6. (−2)⁴: 16 ▶ View Solution
   7. (−10)³: −1 000 ▶ View Solution
   8. (−5)²: 25 ▶ View Solution

5. Mixed Operations

   1. (−3) × 4 + 5: −7 ▶ View Solution
   2. 10 ÷ (−2) + 8: 3 ▶ View Solution
   3. (−6) × (−2) − 15: −3 ▶ View Solution
   4. (−20) ÷ 4 × (−3): 15 ▶ View Solution
   5. 3 × (−5) + 2 × 7: −1 ▶ View Solution
   6. (−4)² − 20: −4 ▶ View Solution

6. True or False

   1. (−3) × (−4) = −12: False — result is 12 ▶ View Solution
   2. Negative × positive is always negative: True ▶ View Solution
   3. (−1)³ = 1: False — result is −1 ▶ View Solution
   4. Negative ÷ negative is always positive: True ▶ View Solution
   5. (−6)² = −36: False — result is 36 ▶ View Solution
   6. Product of three negatives is negative: True ▶ View Solution

7. Find the Missing Number

   1. (−4) × ___ = 28: −7 ▶ View Solution
   2. ___ ÷ (−3) = 7: −21 ▶ View Solution
   3. ___ × (−5) = −40: 8 ▶ View Solution
   4. (−36) ÷ ___ = −9: 4 ▶ View Solution
   5. ___ × (−6) = 54: −9 ▶ View Solution
   6. 24 ÷ ___ = −8: −3 ▶ View Solution

8. Temperature Changes

   1. Change (−3°C × 5 days): −15°C ▶ View Solution
   2. Drop per day (−24°C over 6 days): −4°C per day ▶ View Solution
   3. Drop per step (3 equal steps, total −15°C): −5°C each ▶ View Solution
   4. Change (−2°C × 8 hours): −16°C ▶ View Solution

9. Money and Debt

   1. Total loss (−$150/week × 4 weeks): −$600 ▶ View Solution
   2. Monthly repayment (−$360 ÷ 6 months): −$60 per month ▶ View Solution
   3. Days to repay $21 at $3/day: 7 days ▶ View Solution
   4. Total depth (−8 m × 7 minutes): −56 metres ▶ View Solution

10. Exam Challenge

    1. Why even number of negatives gives positive: Each pair of negatives multiplies to positive — all pairs cancel, leaving positive ▶ View Solution
    2. Can (−a) × (−b) be negative: No — same signs always give positive ▶ View Solution
    3. (2, −6), (3, −4), (4, −3), (6, −2), (−2, 6), (−3, 4), (−4, 3), (−6, 2) ▶ View Solution
    4. (−2)⁶: 64 ▶ View Solution