Page 23 - ArithBook5thEd ~ BCC

For the hundreds place, 4 × 2 hundreds is 8 hundreds,to which we add the 2 hundreds that were
carried. This gives us 10 hundreds,or 1 thousand.We put down 0 in the hundreds place, and 1 in the
thousands place.

{2}
251
× 4
10 0 4

The product of 251 and 4 is 1004.

If the multiplier has more than one digit, the procedure is a little more complicated. We get partial
products (one for each digit of the multiplier) which are added to yield the total product.

Example 17. Consider the product

24
× 32

Since the multiplier stands for 3 tens +2 ones, we can split the product into two partial products

24
× 2
48

and

24

× 3
Notice that in the second partial product the multiplier is in the tens column. This is almost exactly
like having a 1-digit multiplier. The second partial product is obtained by simply putting down a 0 in
the ones place and shifting the digit products one place to the left:

24
× 3
72 0

(Notice that we put down 2 and carried 1 when we performed the digit product 3 × 4= 12.) The total
product is the sum of the two partial products: 48 + 720 = 768. We can write the whole procedure
compactly by aligning the two partial products vertically

24

× 32
48
72 0

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