Readings for Session 9 – (Continued)  

Array Models for Multiplication of Whole Numbers

Repeated Addition Definition for Multiplication of Whole Numbers. Given a whole number a ≠ 0 of equal sets, each containing b elements, we define 0 ∙ b = 0 and

The numbers a and b are called factors and ab is the product.

Notations used for multiplication:  ab = a ∙ b = a × b = a * b = (a)(b).

Example:  The product 42 × 5 may be thought of as 42 + 42 + 42 + 42 + 4

 

Array Models

     Another model for multiplication of whole numbers is the sets may be interpreted as an array of rows and columns. Usually in mathematics, rows are horizontal and columns are vertical.

Example:  What is the area of a region that measures three feet by eight feet?

The product 3 × 8 may be illustrated as three rows of eight items, as in this figure with 3 rows of 8 squares each: 

 

     This is repeated addition since each row may be considered to be a set, so the cardinality of the union of the three disjoint sets gives us 3 × 8 = 8 + 8 + 8 = 24.
The area of the region is twenty-four square feet.

Example:  How many children are in a room with fourteen children in each of three rows? 

Since 3 × 14 = 14 + 14 + 14 = 42, there are 42 children in the room.

   

      

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