The multiplication process with a multiple digit multiplier
In a multiplication in which the multiplier is composed of two or more digits, the
multiplication must take place in parts . The process is as follows:
First Partial Product Multiply the multiplicand by the ones digit of the multiplier. This product is called the
first partial product .
Second Partial Product Multiply the multiplicand by the tens digit of the multiplier. This product is called the
second partial product . Since the tens digit is used as a factor, the second partial product is written below the first partial product so that its rightmost digit appears in the tens column.
If necessary, continue this way finding partial products. Write each one below the previous one so that the rightmost digit appears in the column directly below the digit that was used as a factor.
Total Product Add the partial products to obtain the
total product .
It may be necessary to carry when finding each partial product.
Sample set c
Multiply 326 by 48.
This step is unnecessary since all of the digits in the multiplier have been used.
Add the partial products to obtain the total product.
Since 0 times 1508 is 0, the partial product will not change the identity of the total product (which is obtained by addition). Go to the next partial product.
Often, when performing a multiplication, one or both of the factors will end in zeros. Such multiplications can be done quickly by aligning the numbers so that the rightmost nonzero digits are in the same column.
Sample set d
Perform the multiplication
.
Since 9 and 2 are the rightmost nonzero digits, put them in the same column.
Draw (perhaps mentally) a vertical line to separate the zeros from the nonzeros.
Multiply the numbers to the left of the vertical line as usual, then attach to the right end of this product the total number of zeros.
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