Multiplying Integers Using the Even and Odd Rule

🔑 Key Concepts

• Multiplying two integers with the same sign results in a positive product.
• Multiplying two integers with different signs results in a negative product.
• An even number of negative factors results in a positive product.
• An odd number of negative factors results in a negative product.
• Follow the order of operations when multiplying integers in expressions.

✏️ Worked Examples – Multiplying Integers

Understanding the Rule for Negative Numbers

Count the number of negative factors before multiplying.

Even number of negatives → Positive product

Odd number of negatives → Negative product

After determining the sign, multiply the absolute values of the factors.

Example – Even Number of Negatives

\(\displaystyle (-6)(-2)(3)\)

Step 1: Count the negative factors.

There are 2 negative numbers.

Step 2: Determine the sign.

Two negatives is an even number, so the product will be positive.

Step 3: Multiply the absolute values.

\(\displaystyle 6\times2\times3=36\)

Final Answer:

\(\displaystyle (-6)(-2)(3)=36\)

Example – Odd Number of Negatives

\(\displaystyle (-4)(-5)(-2)\)

Step 1: Count the negative factors.

There are 3 negative numbers.

Step 2: Determine the sign.

Three negatives is an odd number, so the product will be negative.

Step 3: Multiply the absolute values.

\(\displaystyle 4\times5\times2=40\)

Final Answer:

\(\displaystyle (-4)(-5)(-2)=-40\)

🧠 Math Vocabulary

• Integer: A whole number that can be positive, negative, or zero.
• Product: The result of multiplication.
• Factor: A number being multiplied.
• Negative Number: A number less than zero.
• Order of Operations: The rules that tell the correct sequence to evaluate expressions.

💡 Main Idea

When multiplying integers, the most important step is determining the sign of the answer. Count the number of negative numbers in the problem. If the number of negatives is even, the product will be positive. If the number of negatives is odd, the product will be negative. After determining the sign, multiply the numbers as usual.

📚 What You Should Already Know

You should know how to multiply basic whole numbers and understand the difference between positive and negative numbers on a number line.

🚀 What Comes Next

Next, students will apply integer multiplication within multi-step expressions using the order of operations and begin working with integer division and real-world applications involving positive and negative values.

🧩 Embed This Video in Your LMS

Teachers can embed this YouTube video directly into Canvas, Google Classroom, Schoology, or another learning platform. Click below to show the embed code.