## Understanding How to Multiply and Divide Negative Numbers

##### Introduction to Multiplying and Dividing Negative Numbers

Understanding how to multiply and divide negative numbers is a fundamental skill in mathematics. These operations are essential for solving various problems in algebra and beyond. This guide will help you grasp the concepts and rules, making it easier to handle negative numbers confidently.

###### Multiplying Negative Numbers

When multiplying negative numbers, the key rule to remember is that multiplying two negative numbers results in a positive number. Conversely, multiplying a negative number by a positive number (or vice versa) results in a negative number.

**Explanation:**

If both numbers are negative, their product is positive.

If one number is negative and the other is positive, their product is negative.

**Example:**Let's say we need to multiply -3 and -4.

Step 1: Identify the signs of the numbers. Both numbers are negative. Step 2: Multiply the absolute values (ignore the signs for a moment). 3 times 4 equals 12. Step 3: Since both numbers were negative, the product is positive. Therefore, -3 times -4 equals 12. ✨

###### Dividing Negative Numbers

The rules for dividing negative numbers are similar to those for multiplication. The result's sign depends on the signs of the numbers being divided.

**Explanation:**

If both numbers are negative, their quotient is positive.

If one number is negative and the other is positive, their quotient is negative.

**Example:**Let's divide -12 by -3.

Step 1: Identify the signs of the numbers. Both numbers are negative. Step 2: Divide the absolute values. 12 divided by 3 equals 4. Step 3: Since both numbers were negative, the quotient is positive. Therefore, -12 divided by -3 equals 4. 🎉

###### Friendly Example: "The Temperature Drop"

Imagine it's a chilly winter day. The temperature drops 3 degrees each hour. If it drops for 4 hours, what is the total change in temperature?

Step 1: The temperature drop each hour is -3 degrees. Step 2: Multiply the hourly drop by the number of hours. So, -3 degrees times 4 hours equals -12 degrees. ❄️

Now, if the temperature dropped by -12 degrees over 4 hours, we can find the average hourly drop by dividing:

Step 3: Divide -12 degrees by 4 hours. This gives -3 degrees per hour.

Using these simple steps and rules, you can easily multiply and divide negative numbers, making your math problems much more manageable!