Multiply (-22) By (-12): Simple Calculation Steps

Let's dive into multiplying these two negative numbers! When we're dealing with multiplication involving negative numbers, it's super important to remember the rules. This article will walk you through the process step by step, so you can easily understand how to solve this type of problem. Get ready to sharpen those math skills!

Understanding the Basics of Multiplying Negative Numbers

When you multiply two negative numbers together, the result is always a positive number. Think of it this way: a negative times a negative cancels each other out, resulting in a positive. This is a fundamental rule in mathematics and is crucial for solving problems like the one we have here: (-22) * (-12).

To break it down further, consider the number line. Multiplying by a negative number can be seen as flipping the direction on the number line. So, if you're starting with a negative number and multiplying by another negative number, you're essentially flipping the direction twice, which brings you back to the positive side. Understanding this concept can make multiplying negative numbers much more intuitive.

Now, let's put this into practice. Imagine you have -22 and you need to multiply it by -12. You can think of it as taking -22, twelve times, but in the opposite direction (because of the -12). Each time you add -22 in the opposite direction, you're moving towards the positive side of the number line. After doing this twelve times, you'll end up with a positive number. This positive number is the answer to our multiplication problem.

Another way to understand this is by relating it to real-world scenarios. For example, think about owing money. If you owe $22 (-22) to twelve different people (-12), the total amount you don't have (the absence of debt) becomes a positive asset in a way. This analogy helps to visualize how two negatives can result in a positive outcome. The key takeaway here is that multiplying two negative numbers yields a positive result. This rule is consistent and applies to all real numbers, making it a cornerstone of arithmetic and algebra.

Step-by-Step Calculation of (-22)(-12)

Let's calculate the result of multiplying -22 by -12. First, remember the rule: a negative number multiplied by a negative number results in a positive number. So, we know our answer will be positive. The next step is to multiply the absolute values of the numbers, which are 22 and 12.

To multiply 22 by 12, you can use the standard multiplication method. Start by multiplying 22 by 2 (the digit in the ones place of 12). That gives you 44. Next, multiply 22 by 1 (the digit in the tens place of 12). That gives you 22. Since we are multiplying by 10 (because it's in the tens place), we add a zero to the end, making it 220.

Now, add the two results together: 44 + 220. This equals 264. Therefore, the result of multiplying 22 by 12 is 264. Since we initially determined that the answer would be positive (because we are multiplying two negative numbers), our final answer is positive 264.

Alternatively, you can break down the numbers to make the multiplication easier. For example, you can multiply 22 by 10 and then multiply 22 by 2, and then add the results together. So, 22 * 10 = 220, and 22 * 2 = 44. Adding these together gives you 220 + 44 = 264. This method can be particularly helpful if you find it easier to work with smaller numbers.

Another useful technique is to use the distributive property. You can express 12 as (10 + 2), so the problem becomes -22 * (10 + 2). Using the distributive property, you multiply -22 by each term inside the parentheses: (-22 * 10) + (-22 * 2). This simplifies to -220 + (-44), which equals -264. However, remember that we are multiplying -22 by -12, so the final answer is positive 264. Keeping track of the signs is crucial in these calculations!

Common Mistakes to Avoid

When multiplying negative numbers, there are a few common mistakes to watch out for. One of the most frequent errors is forgetting the rule that a negative times a negative equals a positive. It's easy to accidentally keep the negative sign, especially if you're working quickly. Always double-check the signs before finalizing your answer. If you multiply -22 and -12, make sure you remember that the result will be positive 264, not negative.

Another mistake is making errors in the multiplication itself. Double-check your calculations to ensure you haven't made a simple arithmetic mistake. Sometimes, under pressure or when working quickly, it’s easy to miscalculate. It's a good practice to review your work or even use a calculator to verify your answer, especially if you're unsure.

Confusion with addition and subtraction rules can also lead to errors. Remember, the rules for multiplying and dividing negative numbers are different from those for adding and subtracting them. For instance, adding two negative numbers results in a negative number (e.g., -5 + -3 = -8), whereas multiplying two negative numbers results in a positive number. Keeping these rules distinct is crucial.

Furthermore, be careful when dealing with multiple negative signs in a single problem. If you have a series of multiplications involving negative numbers, take it one step at a time. Determine the sign of the final result first, and then perform the multiplication. This can help prevent confusion and ensure you get the correct answer.

Lastly, ensure that you understand the problem correctly before attempting to solve it. Misreading the question or misunderstanding what is being asked can lead to an incorrect answer, even if your calculations are accurate. Taking a moment to fully comprehend the problem can save you time and prevent unnecessary errors. Practice and attention to detail are key to mastering these concepts.

Conclusion

In summary, multiplying -22 by -12 involves understanding the fundamental rule that the product of two negative numbers is positive. By multiplying the absolute values 22 and 12, we get 264. Therefore, (-22)(-12) = 264. Keeping the rules for multiplying negative numbers clear can help you avoid common mistakes and confidently solve similar problems.

So, the correct answer is:

D. 264

For more information on multiplication rules, you can check out this resource on Math is Fun https://www.mathsisfun.com/multiplying-negatives.html.