which choice shows the product of 22 and 49

Daniel Parker

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27-02-2025

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Which Choice Shows the Product of 22 and 49? A Step-by-Step Guide to Multiplication

This article will guide you through finding the product of 22 and 49, explaining the process clearly and demonstrating different methods for solving this multiplication problem. We'll cover standard multiplication, breaking down the numbers, and even using estimation to check your answer.

Understanding the Problem

The question "Which choice shows the product of 22 and 49?" is asking for the result of multiplying 22 by 49. The product in mathematics refers to the answer you get when you multiply two or more numbers together.

Method 1: Standard Multiplication

The most common method is standard long multiplication. This involves multiplying each digit of one number by each digit of the other, then adding the results together.

Here's how to do it for 22 x 49:

1. Multiply 22 by 9:

   • 22 x 9 = 198 (9 x 2 = 18, write down 8 carry-over 1; 9 x 2 + 1 = 19)

2. Multiply 22 by 40:

   • 22 x 40 = 880 (Think of it as 22 x 4 = 88, then add a zero because you're multiplying by 40)

3. Add the results:

   • 198 + 880 = 1078

Therefore, the product of 22 and 49 is 1078.

Method 2: Breaking Down the Numbers

We can simplify the multiplication by breaking down the numbers into smaller, easier-to-manage parts.

• Break down 22: 22 can be expressed as 20 + 2.
• Break down 49: 49 can be expressed as 40 + 9.

Now, we can multiply each part separately:

1. 20 x 40 = 800
2. 20 x 9 = 180
3. 2 x 40 = 80
4. 2 x 9 = 18

Now add all the results together: 800 + 180 + 80 + 18 = 1078

Again, the product of 22 and 49 is 1078.

Method 3: Estimation (Checking Your Answer)

Before calculating, you can estimate the answer to check if your result is reasonable.

• Round 22 to 20.
• Round 49 to 50.

20 x 50 = 1000. Our answer of 1078 is close to 1000, suggesting it's likely correct. Estimation helps to catch major calculation errors.

Conclusion

Through various methods – standard multiplication, breaking down numbers, and estimation – we've confirmed that the product of 22 and 49 is 1078. Remember, choosing the correct method depends on your comfort level and the specific problem at hand. The key is to understand the fundamental concept of multiplication and apply the method consistently. Practice regularly to improve your multiplication skills.