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

= 3640

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. 

We write the above computation in a vertical form (this form is called partial products) and rewrite the computation in the standard form.

  

      

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