2.1 Multiplication of whole numbers  (Page 2/3)

Practice set b

Find the following products.

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:

• Part 1 First Partial Product Multiply the multiplicand by the ones digit of the multiplier. This product is called the first partial product .
• Part 2 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.
• Part 3 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.
• Part 4 Total Product Add the partial products to obtain the total product .

Sample set c

Practice set c

Multiplications with numbers ending in zero

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 $(\text{49},\text{000})(\mathrm{1,}\text{200})$ .

$\begin{array}{ccc}\text{(49,000)(1,200)}& =& \hfill \text{49000}\\ & & \hfill \underline{\times \mathrm{ 1200}}\end{array}$

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.

The product is 58,800,000

Practice set d

Calculators

Most multiplications are performed using a calculator.