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solve the multiplication problem 23*27 by writing equations that use expanded forms and the distributed property. relate the equation to the steps in partial-products algorithm for calculating 23*27. Use this to explain why the partial-products algorithm calculates the correct answer to 23*27.
What is a "partial-products algorithm?" Do you perhaps mean something like this: (20 + 3)(20 + 7)?Quote:
Originally Posted by green11
-Dan
no, something like this
partial produce algorithm example
Original problem
764
x58
------
764
x58
-------
32-8*4
480-8*60
5,600-8*700
200-50*4
3,000-*50*60
35,000-50*700
44,312(total after adding the amounts, 32+480...)
Dan's interpretation of your problem is correct.
We can consider the product of (764)x(58) as (700 + 60 + 4) x (50 + 8) = (8+50) x (4 + 60 + 700) by commutativity of addition and multiplication
(8+50) x (4+60+700) using foil method / distributive property is 8*4 + 8+60 + 8*700 + 50*4 + 50*60 + 50*700
For 23 x 27 it's exactly the same process and you start with the form Dan outlined for you already.