Reducing Fractions

       
           

We have been studying the fractions from our elementary classes that they are represented in A /B form. Where, A and B or numerator and denominator respectively are the two parts of the fraction. For instance, 45 /59 represent a fraction with 45 as numerator and 59 as the denominator. reducing fractions by dividing the top and the bottom part by the same numbers is mathematically possible. It is always not possible to reduce the fraction. The reduced fraction represents the equivalent fraction of the original one. It is similar to writing a number in the form of its multiples. The same way we reduce a fraction by writing the numerator and the denominator of a fraction in the form of their multiples. The common multiples are cancelled from the top and the bottom to get the reduced fraction.

So, to reduce fractions means to write them in their lower terms.

 

For example, if we have a reducing fraction 1024 /5124, we can reduce it by either dividing each of the numerator and the denominator by their common multiple or by factorizing them. Let us factorize the two numbers 1024 and 5124. 1024 can be written as: 1024 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 and 5124 can be factorized as follows: 5124 = 2 * 2 * 3 * 7 * 61.

Replacing the numerator and the denominator by their respective factors we write the fraction as:

1024 / 5124 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 /2 * 2 * 3 * 7 * 61

Here we see that the Greatest common factor in the numerator and the denominator is 2 * 2 = 4. Removing it we get:

1024 / 5124 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 / 3 * 7 * 61 = 256 /1281

256 / 1281 is further not possible to be reduced. Also the fraction 256 /1281 represents the equivalent fraction of 1024 / 5124.

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Math Topics