Step 3: Sum Partial Products for the Total Product
Grade 4 Eureka Math students complete multi-digit multiplication using the area model by summing all partial products to get the total product. After computing each rectangle's area separately, students add them: for 30 × 25, the partial products 600 and 150 add to 750. For 40 × 38, partial products 1,200 and 320 add to 1,520. This final summation step ties together the decomposition work and demonstrates that the whole product equals the sum of its parts, directly mirroring the distributive property.
Key Concepts
To find the total product, add the partial products together. $$Total\ Product = Partial\ Product 1 + Partial\ Product 2$$.
Common Questions
What is the final step in the area model for multiplication?
Add all the partial products together to get the total product.
How do you find the total product for 30 times 25?
Partial products are 30 × 20 = 600 and 30 × 5 = 150. Sum: 600 + 150 = 750.
How do you find the total product for 40 times 38?
Partial products are 40 × 30 = 1,200 and 40 × 8 = 320. Sum: 1,200 + 320 = 1,520.
What mathematical property does summing partial products demonstrate?
The distributive property: a × (b + c) = a × b + a × c. Partial products compute each term separately, then sum them.
How does this step connect to the standard algorithm?
In the standard algorithm, carrying performs the same addition of partial products but compresses it into one vertical computation.