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Division with negative numbers can seem tricky, but it's simple once you understand the rules. When dividing, follow these rules:

• If you divide a negative number by a positive number, the result is negative.
• If you divide a positive number by a negative number, the result is also negative.
• If you divide two negative numbers, the result is positive.

In the example \(\frac{-72}{9}\), we have a negative numerator and a positive denominator. According to the rules, this gives a negative result. So, \(-72 \div 9 = -8\). Remember, the division itself operates just like any other division; the sign of the result is determined by the rules above.

Verifying your division result is crucial to ensure accuracy. After completing the division, you should always multiply the quotient (result of division) by the denominator to check if you get back the numerator. Let's see this step-by-step for the division problem \(\frac{-72}{9}\):
After dividing, we got \(-8\) as the quotient. To verify, multiply the quotient by the denominator: \(-8 \times 9\). Performing the multiplication: \(-8 \times 9 = -72\), which brings us back to our original numerator. Thus, the division is verified correctly. Verification is an excellent habit as it builds confidence that your calculations are accurate.

Breaking problems into smaller, manageable steps can help make them easier to solve. Here's how you can solve division problems step-by-step, like in the exercise:
Step 1: Identify the components of your division problem. For \(\frac{-72}{9}\), the numerator is \(-72\) and the denominator is \(\text{9}\).
Step 2: Perform the division. Divide the numerator by the denominator: \(-72 \div 9\). Calculate the result, which is \(-8\).
Step 3: Verify the result by multiplying the quotient by the denominator: \(-8 \times 9\). If this product equals the original numerator (which it does: \(-72\)), your answer is correct.
Repeat these steps for other divisions to ensure accuracy and build your proficiency in handling division problems systematically.