Posts tagged math

Casting Out Nines

Sweet multiplication trick. Don’t let the “mod 9” stuff throw you. Read this, then try a couple examples yourself.

“Casting out nines” is an elementary check of a multiplication which makes use of the congruence 10^n=1 (mod 9). Let decimal numbers be written a=a_n...a_2a_1a_0,b=b_n...b_2b_1b_0, and their product be c=c_n...c_2c_1c_0. Let the sums of the digits of these numbers be a^*, b^*, and c^*. Then a=a^* (mod 9), b=b^* (mod 9), and c=c^* (mod 9). Furthermore ab=a^*b^* (mod 9), so c=c^* (mod 9). So if c and a^*b^* are incongruent (mod 9), the multiplication has been done incorrectly.

For example, 12345×67890=838102050. The sum-of-digits of 12345 and 67890 are 15 and 30, respectively, and the product of these is 450. Similarly, the sum-of-digits of 838102050 is 27. And 450=27=0 (mod 9), so the check shows agreement.

Casting out nines is also an addition test, since a+b=a^*+b^* (mod 9)), and a subtraction test, since a-b=9+a-b (mod 9). It can also be used as a division test for a/b=q+r/b (i.e., a=qb+r) since a^*=q^*b^*+r^* (mod 9).

Casting out nines was transmitted to Europe by the Arabs, but was probably developed somewhere on the Indian subcontinent and is therefore sometimes also called “the Hindu check,” with “Hindu” simply meaning the people of the Indian subcontinent.

The procedure was described by Fibonacci in his Liber Abaci (Wells 1986, p. 74).

source: Weisstein, Eric W. ”Casting Out Nines.” From MathWorld—A Wolfram Web Resource.

mathworld.wolfram.com

Growth of numbers (as Holons, each with specific layers). The real Pascal triangle (with hidden information) Some intense math to kick off the weekend. “I’ve never felt so envious of the beautiful mind that created this, yet so sorry for the waste of time.” - Whitney

Growth of numbers (as Holons, each with specific layers).

The real Pascal triangle (with hidden information)

Some intense math to kick off the weekend.

“I’ve never felt so envious of the beautiful mind that created this, yet so sorry for the waste of time.” - Whitney

mu6.com

Miller-McCune: Middle School Music Lessons Enhance Algebra Skills

WILD ABOUT MATH

One of the greatest rewards of working with RRR is networking and developing relationships with other educators.  While working on our Pi Day info, I came across Sol Lederman’s  “Wild About Math” blog.

Sol rarely plugs commerical sites, but he likes what we’re doing and gave us a nice article on the blog that you can read here:  Wild About Math.  We’re flattered that he’d extend that opportunity to us, and encourage you to stop by his site and have a look at all the great math resources he has.

Thanks again, Sol.  We’re Wild About Math!

-Taunia

Math Blogs - Pi Day & more!

While researching for Pi Day, we came across some great math blogs that we thought we’d share with you.  All of these blogs help promote learning math in a fun and creative way, so stop by for some great references and resources:

Wild About Math
Ramblings of a Math Mom
Planet Math
Let’s Play Math!
The Math Mojo Chronicles
Homeschool Math Blog
Math-Blog.com
DreamBox Learning
Tanya Khovanova Math Blog
Kids Math Blog
Learn with Math Games
LazyMaths.com