Partial products or how to break a multiplication problem into two (3rd grade math)
We can think of 8 × 7 (for example) as 5 groups of 7 plus 2 groups of 7. In other words, we break down the product 8 × 7 into parts, into "partial products". This is easily illustrated with an array. Using partial products, or multiplying by parts, allows us to do multiplications such as 15 × 7 using mental math. It goes like this: 15 × 7 is 10 × 7 plus 5 × 7, which equals 70 + 35 = 105. There are other ways, too!
See also
Understanding multiplication word problems, part 2
Math Mammoth Grade 3 curriculum