Calculate Partial Products
Calculate Partial Products is a Grade 4 math skill in enVision Mathematics, Chapter 3: Use Strategies and Properties to Multiply by 1-Digit Numbers. Students apply the distributive property to break a multi-digit number into place value parts, multiply each part separately, then sum the partial products.
Key Concepts
The partial products algorithm uses the distributive property to solve multiplication. A multi digit number is broken into the sum of its place values (expanded form), and each part is multiplied separately before adding the results. $$a \times (b + c + d) = (a \times b) + (a \times c) + (a \times d)$$ Each partial product can be represented as a section of an array, showing how the total product is composed of smaller, manageable parts.
Common Questions
What are partial products in multiplication?
Partial products are the individual results you get when you multiply a single digit by each place value of the other factor. You then add all partial products to get the final answer.
How do you calculate partial products?
Break the multi-digit number into its place value parts (expanded form), multiply the single-digit number by each part, and add all results. For example, 47 times 6: (6 times 7) plus (6 times 40) equals 42 plus 240 equals 282.
How does the area model relate to partial products?
Each partial product corresponds to the area of a rectangle in an area model. The total product is the sum of all these smaller rectangular areas.
What is an example of calculating partial products?
To calculate 3 times 412: 3 times 2 equals 6, 3 times 10 equals 30, 3 times 400 equals 1200. Add: 6 plus 30 plus 1200 equals 1236.
What chapter covers partial products in enVision Mathematics Grade 4?
Calculating partial products is covered in Chapter 3: Use Strategies and Properties to Multiply by 1-Digit Numbers in enVision Mathematics Grade 4.