How is multiplication using partial products different from multiplication using regrouping and how are they similar

Multiplication using partial products is the process of multiplying the ones first, tens next, hundreds next and so on. and finally adding all the products.

Ex:

15 × 75 = 15 × (70 + 5)

= (15 × 70) + (15 × 5)

= 1050 + 75

= 1125

Multiplication using regrouping is the process of carrying over the tens, hundreds, thousands, and so on. to the next level and adding them to the subsequent products.

Ex:

15 × 75 =

75

105

----------

1125

MrRoyal MrRoyal · Answer 2 · 2021-10-24T10:06:43-04:00

Multiplication involves calculating the product of a set of numbers or expressions.

Partial products and multiplication by regrouping are different because partial product involves step by step, while multiplication by regrouping involves direct multiplication.
They are similar because, both methods carry the remainder of a product onto the next.

An illustration of partial product is as follows:

\(\mathbf{39 \times 4}\)

Start by rewriting 39 as 30 + 9

\(\mathbf{39 \times 4 = (30 + 9) \times 4}\)

Expand

\(\mathbf{39 \times 4 = 30 \times 4+ 9 \times 4}\)

Calculate the product

\(\mathbf{39 \times 4 = 120+ 36}\)

\(\mathbf{39 \times 4 = 156}\)

The above product by regrouping is as follows

\(\mathbf{39 \times 4}\)

Start by multiplying 9 and 4

\(\mathbf{9 \times 4 = 36}\)

Write down 6, carry 3

Multiply 3 and 6

\(\mathbf{3 \times 4 = 12}\)

Add the carried 3

\(\mathbf{3 \times 4 +3= 12 +3}\)

\(\mathbf{3 \times 4 +3= 15}\)

So, the complete product is:

\(\mathbf{39 \times 4 = 156}\)