Multiplying and Dividing Negative Numbers

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🎬 Math Angel Video: How to Multiply or Divide Negative Numbers

Rules for Multiplying and Dividing Negative Numbers

Multiplication and division of negative numbers, showing odd negative signs give a negative result and even negative signs give a positive result.

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🛎️ Rules:

When multiplying or dividing negative numbers, the sign of the final result depends on the number of negative signs in the calculation.

  • Odd number of negative signs → Negative result

Example: $5 \times (-3) = -15$ 
5 × 3 = 15, and with one negative sign the answer is −15.

  • Even number of negative signs → Positive result

Example: $(-12) \div (-3) = +4$
12 ÷ 3 = 4, and with two negative signs, the answer is +4.

How to Multiply or Divide 3 Numbers with Negative Signs?

Steps for multiplication and division with rules for odd and even negative signs determining result positivity.

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When there are 3 numbers or more in one calculation, you can work two numbers at a time, from left to right.

 

🛎️ Example 1: Multiplication

$$(-2)\times(-5)\times(-3)=?$$

  • $(-2)\times(-5)=+10$
    Two negative signs → positive result
  • $10\times(-3)=-30$
    One negative sign → negative result
  • Final Answer:

 

🛎️ Example 2: Division

$$(-24)\div 4 \div (-2)=?$$

  • $(-24)\div 4 = -6$
    One negative sign → negative result
  • $-6 \div (-2) = +3$
    Two negative signs → positive result
  • Final Answer: +3

How to Multiply and Divide Negative Numbers (Mixed Operations)

Combining multiplication and division with examples showing the rules for odd and even numbers of negative signs, calculating from left to right.

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When a calculation has both multiplication and division, you calculate from left to right, two numbers at a time.

 

🛎️ Example 1:

$$(-28) \div 4 \times (-3)=?$$

  • $(-28) \div 4 = -7$
    One negative sign → negative result
  • $ -7 \times (-3) = +21$
    Two negative signs → positive result
  • Final Answer: 21

 

🛎️ Example 2:

$$(-15) \times (-3) \div (-5) = ?$$

  • $(-15) \times (-3) = +45$
    Two negative signs → positive result
  • $45 \div (-5)= -9$
    One negative sign → negative result
  • Final Answer:

🍪 Practice: Multiplying and Dividing Negative Numbers

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Multiplying and Dividing Negative Numbers

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Q: Simplify: $7 \times (-2)$.

2 / 6

Q: Simplify: $(-8) \div 4 \times (-2)$.

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Q: Simplify: $(-6) \div 2 \times (-5)$.

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Q: Simplify: $(-6) \div 2 \times (-4) + (-3)$.

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Q: Simplify: $(-15) \div (-3) \times (-5) + (-4)$.

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Q: Simplify: $(-24) \div (-3) \times (-2) + (-6) \times (-1) $.

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