Definition
Partial product
A partial product is the result of multiplying selected place-value parts of the factors.
What it means
Split each factor by place value, such as 34 = 30 + 4. Multiply every needed pair of parts. Each result is one partial product. Add the partial products to rebuild the complete product.
Remember it
Split, multiply every pair, add the pieces.
Example
For 34 × 27, use (30 + 4)(20 + 7). The partial products are 600, 210, 80, and 28. Adding them gives 600 + 210 + 80 + 28 = 918.
Watch for
The parts 30 and 4 are not partial products by themselves; they become partial products only after multiplication.
Common mix-up
Do not skip a pair: leaving out 4 × 7 would make the final product 28 too small.
Exact meaning
When one or both factors are decomposed into addends, each multiplication of one part by another is a partial product; the sum of all required partial products equals the full product by the distributive property.