When multiplying 32 and 12 how many partial products will there be
The Correct Answer and Explanation is :
When multiplying 32 by 12 using the partial products method, there will be four partial products. Here’s a breakdown of how we arrive at this answer and an explanation of the method.
Explanation of Partial Products Method
The partial products method involves breaking down the numbers being multiplied into smaller, more manageable parts. For the numbers 32 and 12, we can decompose them based on their place values:
- 32 can be split into 30 (the tens place) and 2 (the units place).
- 12 can be split into 10 (the tens place) and 2 (the units place).
Now, we will multiply each part of the first number (32) by each part of the second number (12):
- Multiply 30 (from 32) by 10 (from 12):
[ 30 \times 10 = 300 ] - Multiply 30 (from 32) by 2 (from 12):
[ 30 \times 2 = 60 ] - Multiply 2 (from 32) by 10 (from 12):
[ 2 \times 10 = 20 ] - Multiply 2 (from 32) by 2 (from 12):
[ 2 \times 2 = 4 ]
Summing the Partial Products
After calculating the four partial products, we need to add them together to find the final product:
[
300 + 60 + 20 + 4 = 384
]
Conclusion
In conclusion, when using the partial products method to multiply 32 by 12, we generate four distinct partial products (300, 60, 20, and 4). This method not only simplifies the multiplication process by breaking it into smaller steps but also reinforces the understanding of place value. The final answer, 384, can be confirmed by direct multiplication. Thus, using partial products effectively helps in grasping the concept of multiplication more thoroughly.