Multiplying numbers arranged on top of each other generally refers to long multiplication, a method used to multiply larger numbers. Here's a breakdown of how it works:
Long Multiplication: Step-by-Step
Here's how to perform long multiplication:
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Write the Numbers: Place the numbers on top of each other, aligning them by their place values (ones, tens, hundreds, etc.). Typically, the larger number is placed on top.
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Multiply by the Ones Digit: Multiply each digit of the top number by the ones digit of the bottom number, starting from the right. Write the result below, aligning the ones digit of the product with the ones digit of the bottom number you're multiplying by. If the result is a two-digit number, carry over the tens digit.
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Multiply by the Tens Digit: Multiply each digit of the top number by the tens digit of the bottom number. Write the result below the previous result, but shifted one place to the left (add a zero as a placeholder in the ones place). Carry over as needed.
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Repeat for Remaining Digits: Continue this process for each digit in the bottom number, shifting each subsequent result one place further to the left.
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Add the Partial Products: Add all the partial products you've calculated. The sum is the final product.
Example
Let's multiply 123 by 45:
123
x 45
------
615 (123 x 5)
+ 4920 (123 x 40, which is 123 x 4 with a zero added)
------
5535Therefore, 123 x 45 = 5535.
Key Points
- Place Value: Understanding place value is crucial for correct alignment.
- Carrying Over: Remember to carry over digits when the product of two digits is greater than 9.
- Adding Placeholder Zeros: Shifting each subsequent product one place to the left is the same as adding a zero as a placeholder.
- Practice: The best way to master long multiplication is through practice.
