Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Greatest Multiple in Division

Name: Elaine 
Status: educator
Grade: 9-12
Country: Canada
Date: Summer 2013


Question:
I enjoyed a short article by Vince Calder (on your site) on fast multiplication algorithms. In the last paragraph, the author indicated that there is a similar algorithm for long division that eliminates the necessity of finding the greatest multiple in division. The author indicated that this is very "cool". I would love to read about it, but I could not find it on your site at all.



Replies:
This is a little tricky to format with the limited fonts available but here goes. Consider: 23 / 19 = 1.210526316… (irrational, so the digits keep going without a remainder or a repeating decimal). 1 .1 2 1 .1 1 02 ----.-------------------------------------------------------------------------------------------------------------- 19 ) 23.0 0 0 19 4 0 1 9 2 1 since 21 > 19, divide again in the same column (Remember, each place is a factor of 1/10 the previous column 19 2 0 since 2 < 10, bring down a “0” from the next column to the right 19 10 since 1 < 10 so bring down a “0” from the next column to the right, but 10 is still < 19 so the only divisor is “0”, so bring down another “0” 0 100 use a trial divisor of “2” 38 62 since 19 < 62 use another trial divisor, let’s say “2” again 38 24 since there is no divisor giving a positive remainder i.e. 19 < 24 the only trial divisor is “1” 19 5…. Now add all the trial divisors in each column. This gives 1.2105 …. You just keep going with trial divisors in a given column, and add the columns. The remainders must be less than or equal to “0”, or repeating, never negative. But you need not use the “greatest” divisor so long as the remainder is greater or equal to “0”. Hope the formatting does not obscure the simplicity of trial divisors. Vince Calder



Click here to return to the Mathematics Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (help@newton.dep.anl.gov), or at Argonne's Educational Programs

NEWTON AND ASK A SCIENTIST
Educational Programs
Building 223
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: November 2011
Weclome To Newton

Argonne National Laboratory