maddyhelps

Math 8

Math 8 · Worksheets

Multiplying and dividing integers

Ten questions of mixed difficulty, covering Integers. Print it, or work through it on screen — the answer key starts on its own page.

All worksheets

Multiplying and dividing integers

Math 8 · maddyhelps.com

Name
Date
Score
/ 10

Circle the best answer for each question. Show your work in the space provided.

  1. Which expression has the same value as (−24) ÷ 4?

    1. a) 24 ÷ 4
    2. b) 24 ÷ (−4)
    3. c) (−24) × 4
    4. d) (−24) ÷ (−4)

  2. Which product is positive?

    1. a) (−2) × 3 × 1 × 5
    2. b) (−2) × (−3) × (−1) × (−5)
    3. c) (−2) × (−3) × (−1) × 5
    4. d) 2 × (−3) × (−1) × (−5)

  3. (−6) × (−7) equals

    1. a) −13
    2. b) 13
    3. c) 42
    4. d) −42

  4. −3 + 4 × (−2) equals

    1. a) −11
    2. b) −2
    3. c) 11
    4. d) 5

  5. (−5 + 11) ÷ (−2) × 3 equals

    1. a) −1
    2. b) −9
    3. c) 9
    4. d) 1

  6. A diver goes down 3 m every minute. Which integer shows her change in depth after 4 minutes?

    1. a) −12 m
    2. b) −7 m
    3. c) 1 m
    4. d) 12 m

  7. In a quiz, a right answer scores +5 and a wrong answer scores −3. Amir had 6 right and 8 wrong. What was his score?

    1. a) 28
    2. b) 6
    3. c) −6
    4. d) 54

  8. (−56) ÷ (−7) equals

    1. a) −8
    2. b) −49
    3. c) 8
    4. d) 49

  9. Look at the pattern: 3 × (−4) = −12, 2 × (−4) = −8, 1 × (−4) = −4, 0 × (−4) = 0. What comes next, and why?

    1. a) (−1) × (−4) = 4, because the products go up by 4 each time
    2. b) (−1) × (−4) = −5, because the first factor went down by 1
    3. c) (−1) × (−4) = −4, because every product so far is negative or 0
    4. d) (−1) × (−4) = −4, because a negative times a negative is negative

  10. 18 ÷ (−3) − (−4) × 2 equals

    1. a) 14
    2. b) 2
    3. c) −4
    4. d) −14

Answer key · Multiplying and dividing integers

Math 8 · maddyhelps.com

  1. b) 24 ÷ (−4) — (−24) ÷ 4 and 24 ÷ (−4) both equal −6: a negative divided by a positive and a positive divided by a negative both give a negative answer. (−24) ÷ (−4) = 6, because two negatives give a positive — moving the negative sign to the other number is fine, but putting it on both is not.
  2. b) (−2) × (−3) × (−1) × (−5) — Negative factors cancel in pairs, so a product is positive when it has an even number of negative factors. (−2) × (−3) × (−1) × (−5) has four, which make two pairs, so it equals 30. The others have one or three, which leaves a negative without a partner — fewer negatives does not make a product positive.
  3. c) 42 — The product of two negative numbers is positive: (−6) × (−7) = 42. Answering −42 keeps a negative sign, as if two negatives made something more negative, and −13 adds the numbers instead of multiplying them.
  4. a) −11 — Multiply before adding: 4 × (−2) = −8, and −3 + (−8) = −11. Working left to right gives (−3 + 4) × (−2) = −2, and 5 comes from writing 4 × (−2) as +8.
  5. b) −9 — Brackets first: −5 + 11 = 6. Multiplying and dividing share a step, so go left to right: 6 ÷ (−2) = −3, then −3 × 3 = −9. −1 multiplies first, 6 ÷ (−6), but multiplying does not come before dividing — whichever comes first, reading left to right, goes first.
  6. a) −12 m — Going down 3 m is −3, and 4 minutes of it is (−3) + (−3) + (−3) + (−3) = 4 × (−3) = −12 m. 12 m drops the sign, but she is going down, and −7 m adds the 4 instead of multiplying by it.
  7. b) 6 — 6 right is 6 × 5 = 30 and 8 wrong is 8 × (−3) = −24, so the score is 30 + (−24) = 6. 54 counts the wrong answers as points gained, and 28 multiplies all 14 questions by 5 − 3 = 2, as if every question scored both +5 and −3.
  8. c) 8 — (−7) × 8 = −56, so (−56) ÷ (−7) = 8: two negatives divide to a positive, just as they multiply to one. −8 keeps a negative sign, but check it: (−7) × (−8) = 56, not −56.
  9. a) (−1) × (−4) = 4, because the products go up by 4 each time — As the first factor drops by 1, the product goes up by 4: −12, −8, −4, 0, so the next is 4. That is why a negative times a negative is positive — the pattern does not stop or turn round at 0. Assuming the products stay negative ignores a pattern that has been climbing by 4 all along.
  10. b) 2 — Divide and multiply first: 18 ÷ (−3) = −6 and (−4) × 2 = −8. Then −6 − (−8) = −6 + 8 = 2. −14 subtracts 8 instead of subtracting −8, and −4 works from left to right, subtracting before it multiplies.