List the partial products when finding 16 x 22. then find the final product

The Correct Answer and Explanation is:

To find the product of 16 and 22 using the method of partial products, we can break down each number into its place values and then multiply the parts separately. Here’s how it works step by step:

Step 1: Break Down the Numbers

16 can be broken down into 10 and 6 (i.e., ( 16 = 10 + 6 )).
22 can be broken down into 20 and 2 (i.e., ( 22 = 20 + 2 )).

Step 2: Create Partial Products

Now, we will multiply each part of 16 by each part of 22:

Multiply 10 by 20:
[
10 \times 20 = 200
]
Multiply 10 by 2:
[
10 \times 2 = 20
]
Multiply 6 by 20:
[
6 \times 20 = 120
]
Multiply 6 by 2:
[
6 \times 2 = 12
]

Step 3: List the Partial Products

Now we list the partial products we calculated:

( 200 )
( 20 )
( 120 )
( 12 )

Step 4: Sum the Partial Products

Next, we add all the partial products together:

[
200 + 20 + 120 + 12
]

First, add ( 200 + 20 = 220 ).
Then, add ( 220 + 120 = 340 ).
Finally, add ( 340 + 12 = 352 ).

Final Product

Thus, the final product of ( 16 \times 22 ) is ( \mathbf{352} ).

Explanation

The partial products method is a systematic approach to multiplication that helps break down complex calculations into manageable steps. By decomposing numbers into their place values, we simplify the multiplication process, ensuring accuracy at each stage. This method not only aids in computation but also reinforces an understanding of how numbers are constructed.

In this case, breaking 16 into 10 and 6 and 22 into 20 and 2 allows us to compute each part separately. Each multiplication step is straightforward, leveraging the properties of multiplication to yield partial products that are easy to manage. Finally, summing these partial products results in the total, demonstrating how the distributive property works in multiplication. This method is especially useful in educational settings, helping learners visualize and understand multiplication better.