Definition
Long multiplication
Long multiplication is a written method that adds place-aligned partial products.
Continue from this idea into connected AXIO math.
What it means
Split the second factor by place value. For 16, that means 6 ones and 1 ten. Multiply by the ones, then multiply by the ten; the tens row begins one place left because it represents groups of ten. Add the aligned partial products.
Remember it
One row for each place; shift the row to match that place, then add.
Example
First, 243 × 6 = 1,458. Next, 243 × 10 = 2,430, so that row is shifted one place left. Add 1,458 + 2,430 = 3,888. Therefore 243 × 16 = 3,888.
Watch for
The zero in 2,430 carries the ones place for a tens partial product. It records place value; it is not decoration.
Common mix-up
Treating the 1 in 16 as one instead of one ten gives the wrong second partial product.
Exact meaning
Long multiplication is a written multiplication algorithm. It multiplies one factor by each place-value part of the other factor, writes the partial products in aligned columns, and adds them to get the product.