How to Multiply and Divide Negative Numbers

Multiplying and dividing negative numbers is basically the same as it is with positive numbers. The presence of one or more minus signs (–) doesn’t change the numerical part of the answer. The only question is whether the sign of the answer is positive or negative.

Remember the following when you multiply or divide negative numbers:

  • If the two numbers have the same sign, the result is always positive.

  • If the two numbers have opposite signs, the result is always negative.

Sample questions

  1. Solve the following four multiplication problems:

    a. 5 x 6 = ________________
    b. –5 x 6 = ________________
    c. 5 x –6 = ________________
    d. –5 x –6 = ________________

    As you can see from this example, the numerical part of the answer (30) doesn’t change. Only the sign of the answer changes, depending on the signs of the two numbers in the problem.

    a. 5 x 6 = 30
    b. –5 x 6 = –30
    c. 5 x –6 = –30
    d. –5 x –6 = 30
  2. Solve the following four division problems:

    a. 18 / 3 = ________________
    b. –18 / 3 = ________________
    c. 18 / –3 = ________________
    d. –18 / –3 = ________________

    The numerical part of the answer (6) doesn’t change. Only the sign of the answer changes, depending on the signs of the two numbers in the problem.

    a. 18 / 3 = 6
    b. –18 / 3 = –6
    c. 18 / –3 = –6
    d. –18 / –3 = 6
  3. What is –84 x 21?

    –1,764. First, drop the signs and multiply:

    84 x 21 = 1,764

    The numbers –84 and 21 have different signs, so the answer is negative: –1,764.

  4. What is –580 / –20?

    29. Drop the signs and divide (you can use long division):

    580 / 20 = 29

    The numbers –580 and –20 have the same signs, so the answer is positive: 29.

Practice questions

  1. Solve the following multiplication problems:

    a. 7 x 11 = ________________

    b. –7 x 11 = ________________

    c. 7 x –11 = ________________

    d. –7 x –11 = ________________

  2. Solve the following division problems:

    a. 32 / –8 = ________________

    b. –32 / –8 = ________________

    c. –32 / 8 = ________________

    d. 32 / 8 = ________________

  3. What is –65 x 23?

  4. Find –143 x –77.

  5. Calculate 216 / –9.

  6. What is –3,375 / –25?

Following are the answers to the practice questions:

  1. Multiplication problems

    a. 7 x 11 = 77
    b. –7 x 11 = –77
    c. 7 x –11 = –77
    d. –7 x –11 = 77
  2. Division problems

    a. 32 / –8 = –4
    b. –32 / –8 = 4
    c. –32 / 8 = –4
    d. 32 / 8 = 4
  3. –65 x 23 = –1,495.

    First, drop the signs and multiply:

    65 x 23 = 1,495

    The numbers –65 and 23 have different signs, so the answer is negative: –1,495.

  4. –143 x –77 = 11,011.

    Drop the signs and multiply:

    143 x 77 = 11,011

    The numbers –143 and –77 have the same sign, so the answer is positive: 11,011.

  5. 216 / –9 = –24.

    Drop the signs and divide (use long division):

    216 / 9 = 24

    The numbers 216 and –9 have different signs, so the answer is negative: –24.

  6. –3,375 / –25 = 135.

    First, drop the signs and divide:

    3,375 / 25 = 135

    The numbers –3,375 and –25 have the same sign, so the answer is positive: 135.

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