Find Partial Products from a Decomposed Array
Find Partial Products from a Decomposed Array is a Grade 4 math skill in enVision Mathematics, Chapter 3: Use Strategies and Properties to Multiply by 1-Digit Numbers. Students break a rectangular array into smaller sub-arrays by decomposing one dimension, then add the partial products from each sub-array.
Key Concepts
The area of each smaller rectangle in a decomposed array represents a partial product. The total product is the sum of these partial products. For a problem like $a \times (b+c)$, the partial products are the areas of the two smaller rectangles: $(a \times b)$ and $(a \times c)$.
Common Questions
What is a decomposed array in multiplication?
A decomposed array is a rectangular array that has been split into two or more smaller arrays by breaking one side into parts. Each smaller array represents a partial product.
How do you find partial products from a decomposed array?
Split the array by decomposing one factor into place value parts. Calculate the area of each smaller array as a partial product, then add all partial products for the total.
How does a decomposed array connect to the distributive property?
Each smaller array in the decomposition represents one term of the distributive property. The sum of all smaller areas equals the total product, just as a times (b plus c) equals ab plus ac.
What is an example of finding partial products from a decomposed array?
An array of 6 rows by 47 columns can be split into 6 by 40 (240) and 6 by 7 (42). The total product is 240 plus 42 equals 282.
What chapter covers decomposed arrays in enVision Mathematics Grade 4?
Finding partial products from a decomposed array is covered in Chapter 3: Use Strategies and Properties to Multiply by 1-Digit Numbers in enVision Mathematics Grade 4.