The following is a method for multiplying 21x23 that relies on repeatedly doubling numbers (by adding them to themselves):

23

+23

----- 21=16+4+1

46 2

+46

-----

92 4

+92 368

----- 92

184 8 + 23

184 --------

----- 483

386 16

The answer, 483 to the multiplication problem 21*23, is shown on the bottom of the column on the right

Notice that, to use this repeated doubling method, you have to be able to only add; you don't need to know how to multiply.

A. Discuss and explain the method of repeated doubling. Address the following questions in your discussion:

I.What is the significance of the column of the numbers 2,4,8,16?

II.What is the significance of writing 21=16+4+1

III.How are the numbers 368, 92, and 23 chosen for the column on the right. Why do we add those numbers?

B.Use the method of repeated doubling to calculate 26*35. Show your work.

C.Use the method of repeated doubling to calculate 37*51. Show your work.