Practice Maths

Multiplying and Dividing Integers — Solutions

  1. Multiply integers

    1. 3 × (−4): −12 ▶ View Solution
    2. (−5) × 6: −30 ▶ View Solution
    3. (−3) × (−7): 21 ▶ View Solution
    4. 8 × (−9): −72 ▶ View Solution
    5. (−4) × (−4): 16 ▶ View Solution
    6. (−6) × 5: −30 ▶ View Solution
    7. 7 × (−8): −56 ▶ View Solution
    8. (−10) × (−3): 30 ▶ View Solution

  2. Divide integers

    1. (−12) ÷ 3: −4 ▶ View Solution
    2. 20 ÷ (−4): −5 ▶ View Solution
    3. (−18) ÷ (−6): 3 ▶ View Solution
    4. (−36) ÷ 9: −4 ▶ View Solution
    5. 45 ÷ (−9): −5 ▶ View Solution
    6. (−24) ÷ (−8): 3 ▶ View Solution
    7. (−35) ÷ 7: −5 ▶ View Solution
    8. 56 ÷ (−8): −7 ▶ View Solution

  3. 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. (−5)3: −125 ▶ View Solution
    7. (−10)2: 100 ▶ View Solution
    8. (−2)4: 16 ▶ View Solution

  4. Predict the sign and check reasoning

    1. (−8) × (−7) sign: Positive ▶ View Solution
    2. (−6) × 5 × (−2) sign: Positive ▶ View Solution
    3. Is (−3)4 negative?: False — even power gives positive ▶ View Solution
    4. Is (−4) × (−3) = −12 correct?: Incorrect — correct answer: +12 ▶ View Solution
    5. Rule for sign of a product: Even number of negative factors → positive; odd → negative ▶ View Solution

  5. Real-world contexts

    1. 3°C drop per hour for 5 hours: −15°C total change ▶ View Solution
    2. Submarine descends 4 m/min for 6 min: −24 m ▶ View Solution
    3. Company loses $250 per day for 8 days: −$2 000 ▶ View Solution
    4. Balance drops $60/week from $0 to −$300: 5 weeks ▶ View Solution
    5. Temperature rises from −12°C to 0°C over 4 hours: 3°C per hour ▶ View Solution

  6. Mixed multiplication and division

    1. (−3) × (−4) × 2: 24 ▶ View Solution
    2. 5 × (−2) × (−3): 30 ▶ View Solution
    3. (−1) × (−1) × (−1): −1 ▶ View Solution
    4. (−6) × 0: 0 ▶ View Solution
    5. (−72) ÷ (−8): 9 ▶ View Solution
    6. (−90) ÷ 9: −10 ▶ View Solution
    7. 108 ÷ (−12): −9 ▶ View Solution
    8. (−144) ÷ (−12): 12 ▶ View Solution

  7. Find the missing integer

    1. __ × (−5) = 35: −7 ▶ View Solution
    2. (−4) × __ = −28: 7 ▶ View Solution
    3. __ ÷ (−3) = 9: −27 ▶ View Solution
    4. (−36) ÷ __ = −6: 6 ▶ View Solution
    5. __ × (−8) = 64: −8 ▶ View Solution
    6. (−10) × __ = 0: 0 ▶ View Solution

  8. Order of operations with integers

    1. (−3) × 4 + 2: −10 ▶ View Solution
    2. 6 ÷ (−2) + (−5): −8 ▶ View Solution
    3. (−8) × (−2) − 10: 6 ▶ View Solution
    4. (−4)2 − 20: −4 ▶ View Solution
    5. 3 × (−3) + (−3) × (−3): 0 ▶ View Solution
    6. (−2)3 + (−2)2: −4 ▶ View Solution

  9. Worded integer problems

    1. 3 floors down × 5 (50 sec ÷ 10): −15 floors ▶ View Solution
    2. Temperature at −4°C/hr for 6 hr; same if +4°C × −6 hr?: −24°C; yes — same product ▶ View Solution
    3. −7 yards × 4 plays: −28 yards ▶ View Solution
    4. −$800 × 4 weeks: −$3 200 total ▶ View Solution

  10. Error spotting and reasoning

    1. Sam’s error with (−2)3: Incorrect — correct answer: −8 ▶ View Solution
    2. Jess’s claim about negative ÷ negative: Incorrect — e.g. (−6) ÷ (−2) = +3 ▶ View Solution
    3. 3 friends each owe $15: −$45 total ▶ View Solution
    4. Why does (−) × (−) = (+)?: Pattern of (−3) × n increases by 3 each step — continuing past 0 forces the product positive ▶ View Solution