**
Readings for Session 10 – (Continued)
**

**Standard Multiplication Algorithm**

We can use expanded notation
and the properties for whole number addition and multiplication
to multiply large values. The first part of each example
developing the standard algorithm shows each step in the
process. Next, we write the process in a vertical form, called
the partial products algorithm. Finally, we illustrate the
standard multiplication algorithm, which is a short-cut method
for writing partial products.

*
Example:*
Terry’s take-home pay for
each of the past five weeks was $728. How much take-home pay did
Terry earn over the five week period?

5
× 728
= 5(700 + 20 + 8)
Expanded Notation

= 5(8 + 20 + 700) Commutative and Associative Properties of Addition

= 5(8) + 5(20) + 5(700) Distributive Property of Multiplication over Addition

=
40 + 100 + 3500

Terry receive $3640 over the five week period.

Notice that the standard
form is a shortcut method for writing partial products.

*
Example:*
A manufacturer put 158
pieces of candy in each bag. How many pieces of candy would be
in twenty-three bags of the candy?

23
× 158
= (20 + 3)
× 158
Expanded Notation

=
(3 + 20)
× 158
Commutative Property of Addition

=
3(158) + 20(158)
Distributive Property of Multiplication over Addition

=
3(100 + 50 + 8) + 20(100 + 50 + 8)
Expanded Notation

=
3(8 + 50 + 100) + 20(8 + 50 + 100)
Commutative and Associative Property of Addition

=
3(8) + 3(50) + 3(100) + 20(8) + 20(50) + 20(100)
Distributive Prop. of Multiplication over Addition

=
24 + 150 + 300 + 160 + 1000 + 2000

=
3634

Twenty-three bags of candy would contain 3,634 pieces of candy.

Return
to Peil's Homepage | Minnesota
State University Moorhead | Mathematics
Department