Saturday, February 11, 2012

Textbox: Reducing Fractions

One of the biggest obstacles to doing science is the math.  Sometimes it's not so much that the science is hard but that a student has missed out somewhere on a key math skill.  For example, working with fractions and decimals often comes into play when we are converting from units we commonly use in America (like Fahrenheit, miles, and pounds) to the metric system, the units of science and the rest of the world.

This textbox is about reducing fractions.  When we are reducing a fraction like 180/100, we are not changing the number, we are just making it more manageable.  So 9/5 is the same amount as 180/100, but it sure is a lot easier to work with.

The way you get from 180/100 to 9/5 is easy--it basically amounts to dividing it by 1, which gives you the same number.  If you divide both the top and the bottom by the same number, the amount stays the same.  So if you divide both the top and the bottom of 180/100 by 10, the new form of the fraction is 18/10.  You can always chop off the same number of 0's from the top and bottom of a fraction and it stay the same number.  18/10 is easier to handle than 180/100.

Now I notice that 2 goes into both 18 and 10.  So I can reduce the fraction even further.  Both the top and bottom of 18/10 divided by 2 gives you 9/5.  So there you have it.

By the way, 9/5 is called an improper fraction because the number on top is greater than the number on the bottom.  That means this fraction is bigger than 1.  In fact, we could also represent it as 1 and 4/5 (that form is called a mixed fraction).  But it's easier to work with the amount in its "improper" form.

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