Question

Compare partial products and regrouping how the methods are alike and different

Answer 1

Answer:

We get the same answer from both processes.In the end, it is a multiplication process. In partial product we take the values of ones, tens, hundreds in each step and then add them together. In regrouping same thing happens but we do not break them down to processes.

Step-by-step explanation:

In Partial products we multiply the numbers partially and add them together to get the answer. It is easier to explain with an example, lets say we multiply 47 by 3

1) 47

  ×3

--------

  21

2) 47

   ×3

---------

   21

 120 ($(3\times40)$

3) 3 8

    ×3

----------

  +21

  120

-----------

   141

In Regrouping we add the partial products to the next tens,hundreds and so on. We don not write them down and then add later. Lets take the same example and do the multiplication with Regrouping method.

1)2 --------> ($3\times7=21$ write the number in tenth place here)

 47

 ×3

 ___

 __1  --------> ($3\times7=21$ write the number in ones place here)

2)47

  ×3

 ___

 141   ($3\times4=12$ then add the 2 above to get 14)

We get the same answer from both processes.In the end, it is a multiplication process. In partial product we take the values of ones, tens, hundreds in each step and then add them together. In regrouping same thing happens but we do not break them down to processes.

Answer 2

Partial products are different in regrouping in terms of how numbers are clustered from a set equation as a whole delivering it individual but naturally to all the numbers involved in the set. 
Regrouping is just like the commutative or associative property of numbers.
Associative property of addition is used when you want to group addends. This is mainly used to cluster set of numbers or in this case, addends. How do you use the associative property when you break apart addends? Simple you group them using the open and closed parentheses or brackets. Take for an example 1 + 1 + 2 = 4. Using the associative property you can have either (1 + 1) + 2 = 4 or 1 + (1 + 2) = 4 clustered into place.