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Commutative Property of Multiplication with Decimals

The order that you multiply decimals does not affect the product.

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Going Downtown

Credit: Siqbal
Source: http://commons.wikimedia.org/wiki/File:Chicago_Downtown_Aerial_View.jpg
License: CC BY-NC 3.0

Walk around downtown in any major American city, and youll probably find yourself in the midst of a grid. Streets join each other at right angles. Each block is a square. It’s easy to find your way from one place to another. In contrast, European cities seem to have more curving streets, cul-de-sacs, and confusing intersections. Why are American cities so square?

Commutative Commuting

Being built on a grid makes cities easier to navigate. Directions become commutative. It doesn’t matter whether you go north first or west first to reach your destination. As long as you travel a certain distance in each direction, you’ll end up at the right place. This, however, is not generally the case in European cities, most of which expanded organically over thousands of years. The focus of each city was usually a central marketplace, building, or square. Neighborhoods would grow around it, taking shape based on the needs of the people—which meant some roads curved or ended suddenly. To navigate a city in Europe, you need to follow directions carefully. A wrong turn can lose you in a maze of streets and alleys.

Credit: Thomas Holme
Source: http://commons.wikimedia.org/wiki/File:A_Portraiture_of_the_City_of_Philadelphia.JPG
License: CC BY-NC 3.0

American cities, on the other hand, were constructed in empty spaces. The early planners divided land into grids to make it easier to sell. Philadelphia, built in 1683, became America’s first city on a grid. The original map for the city is pictured above. Congress’s passage of the Land Ordinance of 1785 divided the territory of the West and Midwest into even squares. Today, most U.S. cities and towns are based on grids.

See for yourself: http://www.youtube.com/watch?v=HDWIz72UwU4 

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Watch the following videos to compare how the layouts of the city of Chicago and the town of Rothenberg, Germany came to be.

http://www.youtube.com/watch?v=Wnvr0aJ0hgs

http://www.youtube.com/watch?v=bzfXmiXDeIU

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