which choice shows the product of 22 and 49

Charlotte

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01-03-2025

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

Finding the product of two numbers simply means multiplying them together. So, to answer the question "Which choice shows the product of 22 and 49?", we need to perform the multiplication: 22 x 49. Let's explore a few ways to solve this problem.

Method 1: Standard Multiplication

The most straightforward method is standard, long multiplication. This is a great method for understanding the process:

1. Set up the problem: Write 22 on top and 49 below, aligning the digits.

2. Multiply by the ones digit: Multiply 22 by 9 (the ones digit of 49). 9 x 2 = 18. Write down the 8 and carry-over the 1. Then, 9 x 2 (the tens digit of 22) + 1 (carry-over) = 19. This gives you 198.

3. Multiply by the tens digit: Multiply 22 by 4 (the tens digit of 49). 4 x 2 = 8. Write this down below the 8 in 198, shifted one place to the left (because we are multiplying by tens). Then, 4 x 2 = 8. This gives you 880.

4. Add the results: Add 198 and 880 together: 198 + 880 = 1078.

Therefore, the product of 22 and 49 is 1078.

Method 2: Distributive Property

The distributive property allows us to break down the multiplication into smaller, easier steps. Let's use this method:

1. Break down 49: We can rewrite 49 as 50 - 1.

2. Apply the distributive property: 22 x 49 = 22 x (50 - 1) = (22 x 50) - (22 x 1)

3. Calculate: 22 x 50 = 1100 and 22 x 1 = 22

4. Subtract: 1100 - 22 = 1078

Again, we find that the product of 22 and 49 is 1078.

Method 3: Using a Calculator (For Verification)

While it's important to understand the methods, a calculator can quickly verify your answer. Simply enter 22 x 49 and the calculator will display 1078.

Choosing the Correct Answer

When presented with multiple-choice options, simply look for the number 1078. That's the product of 22 and 49, regardless of the method used to calculate it.

Therefore, to summarize, the correct answer to the question "Which choice shows the product of 22 and 49?" is 1078. Understanding the different methods of multiplication will help you solve similar problems effectively.