Fractions: the basics
Words you need to know:

* fraction, numerator, denominator
* equivalent fraction
* simplify, reduce to simplest form
* common denominator,  least common denominator (LCD)

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This is a fraction.
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These are equivalent fractions.
They have the same value. 
To get an equivalent fraction, multiply the numerator and the denominator by the same number. 
     Remember, whatever you do to the top number, you must do the same to the bottom number.  In this example, I multiplied the numerator by 2 and I multiplied the denominator by 2.
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Sometimes you need to reduce a fraction to its simplest form, like this one. 
To simplify a fraction, just divide the numerator and the denominator by the same number (a common factor), until you can't divide anymore. 
     Remember, whatever you do to the top number, you must do the same to the bottom number.  In this example, I divided the numerator by 3 and I divided the denominator by 3.
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When you want to compare two fractions, it's easy if they have the same denominators (common denominators).  You just compare the numerators.  Here, you can see that 3 is less than 5, so 3/8 is less than 5/8. 

But when they have different denominators, what do you do?
Change them into equivalent fractions, with the least common denominator!

To find the least common denominator, you need to know what the least (or lowest) common multiple is for the two denominators. 

Here, the two denominators are 4 and 3.  What is the least common multiple (LCM) of 4 and 3?  12. 
     So you need to make equivalent fractions with 12 as the denominator.
Now it's easy to compare the two fractions.  The denominators are the same, so all you have to do is compare the numerators.  9 is greater than 8, so 9/12 is greater than 8/12,  so 3/4 is greater than 2/3.


A quick hint:
Sometimes, if it takes too long to find the LCM to get the least common denominator, just find a common denominator by multiplying the two numbers together. 

     For example,
I could get the LCD by thinking about the multiples of 8 and 6.
     8:    8, 16, 24, 32, 40, 48, 56, 64, 72, 80, ...
     6:    6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...
The common multiples are 24, 48.  The least common multiple is 24, so the least common denominator is 24.
To review Factors and Multiples, see Little Joe's Math Journal.
OR I could just multiply the two denominators (8x6), and get 48 as a common denominator.

This way is sometimes faster, but if a question asks for the LCD, you must give the least common denominator, not just any common denominator.
Back to Rinaldo's Math Page.
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