How to Multiply and Divide Integers? (+FREE Worksheet!)

Multiplying and dividing integers follows a simple set of sign rules that never change. Once you know whether the answer is positive or negative, the actual multiplication or division is the same as with whole numbers. This lesson covers every sign-rule case, works through four detailed examples, and gives you practice problems to sharpen your skills.

What Are Integers?

An integer is any whole number, its negative counterpart, or zero: …, −3, −2, −1, 0, 1, 2, 3, … Multiplying and dividing integers produces results that are also integers (as long as the division is exact).

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The Sign Rules for Multiplying and Dividing Integers

Only two rules govern the sign of the answer:

Rule 1: Same Signs → Positive Result

When both integers have the same sign (both positive or both negative), the result is positive.

• \(\color{blue}{3 \times 4 = 12}\)  (positive × positive)
• \(\color{blue}{(-3) \times (-4) = 12}\)  (negative × negative)
• \(\color{blue}{(-8) \div (-2) = 4}\)  (negative ÷ negative)

Rule 2: Different Signs → Negative Result

When the two integers have different signs, the result is negative.

• \(\color{blue}{(-6) \times 5 = -30}\)
• \(\color{blue}{8 \times (-7) = -56}\)
• \(\color{blue}{(-48) \div 6 = -8}\)
• \(\color{blue}{56 \div (-7) = -8}\)

Rule 3: Multiplying or Dividing by Zero

Any integer multiplied by \(\color{blue}{0}\) equals \(\color{blue}{0}\). Division by zero is undefined.

Step-by-Step Summary

1. Ignore the signs for a moment and multiply or divide the absolute values.
2. Count the signs: if both are the same, the answer is positive; if different, the answer is negative.
3. Attach the correct sign to your result.

Watch: Integer Multiplication & Division (Video Lesson)

Math Antics explains both operations clearly, with visual sign-rule examples:

Multiplying and Dividing Integers – Worked Examples

Example 1: Find \(\color{blue}{(-3) \times (-4)}\).

Both signs are negative (same sign) → result is positive.
\(\color{blue}{3 \times 4 = 12}\), so \(\color{blue}{(-3) \times (-4) = 12}\).

Example 2: Find \(\color{blue}{(-6) \times 5}\).

Different signs → result is negative.
\(\color{blue}{6 \times 5 = 30}\), so \(\color{blue}{(-6) \times 5 = -30}\).

Example 3: Find \(\color{blue}{(-48) \div 6}\).

Different signs → result is negative.
\(\color{blue}{48 \div 6 = 8}\), so \(\color{blue}{(-48) \div 6 = -8}\).

Example 4: Find \(\color{blue}{(-72) \div (-9)}\).

Same signs (both negative) → result is positive.
\(\color{blue}{72 \div 9 = 8}\), so \(\color{blue}{(-72) \div (-9) = 8}\).

More Practice: Step-by-Step Video Review

Math with Mr. J walks through additional examples of multiplying and dividing integers:

Exercises for Multiplying and Dividing Integers

Apply the sign rules to find each answer.

1. \(\color{blue}{(-5) \times (-6)}\)
2. \(\color{blue}{7 \times (-8)}\)
3. \(\color{blue}{(-3) \times 4 \times (-2)}\)
4. \(\color{blue}{(-48) \div 6}\)
5. \(\color{blue}{(-72) \div (-9)}\)
6. \(\color{blue}{56 \div (-7)}\)

Answers

1. \(\color{blue}{30}\)
2. \(\color{blue}{-56}\)
3. \(\color{blue}{24}\)
4. \(\color{blue}{-8}\)
5. \(\color{blue}{8}\)
6. \(\color{blue}{-8}\)

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Want More Practice?

We haven’t published a worksheet built specifically for Multiplying and Dividing Integers just yet. In the meantime, the free worksheets below cover closely related skills and concepts. If you’d like extra practice, download any that look helpful, complete the problems, and check your work — they’re a great way to reinforce what you learned on this page and strengthen the foundations this topic builds on:

• Download Order of Operations and Evaluating Expressions Worksheet
• Download Rational and Irrational Numbers Worksheet
• Download Properties of Exponents Worksheet

Frequently Asked Questions

Why is a negative times a negative positive?

Multiplying by -1 reverses direction on the number line. Doing it twice returns you to the positive side, so \(\color{blue}{(-1) \times (-1) = 1}\), and the same logic extends to all negative × negative products.

Do the same sign rules apply to division?

Yes. Division and multiplication share identical sign rules: same signs give a positive quotient, different signs give a negative quotient.

What if I multiply more than two integers?

Count the total number of negative factors. An even count gives a positive result; an odd count gives a negative result. For example, \(\color{blue}{(-2) \times (-3) \times (-1) = -6}\) (three negatives → odd → negative).

Related Topics

• Adding and Subtracting Integers
• Integers and Absolute Value
• Order of Operations
• The Distributive Property
• Translate Phrases into an Algebraic Statement