Simplify Fractions: Tips and Tricks for Quick and Easy Simplification

In summary, the conversation discusses ways to simplify fractions, particularly when dealing with larger fractions. The suggested methods include comparing factors and using the Euclidean algorithm to find the greatest common divisor. These methods are more efficient than resorting to trial and error.
  • #1
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I'm wondering about fractions, and how I can simplify them. If they're small like 6/10, I see it straight away, but if they're big like 122/163, I don't really know where to start without resorting to random trial and error...
Isn't there a more structural procedure to simplify fractions as much as possible?
 
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  • #2
the only way I can think of off the top of my head is comparing factors...which is a litle better than trial and error.
ie: factors of 122 include (I'll probably miss some) 1,2,61,122
but the 163 is prime and only has factors of 1,163.
Since no factors (besides 1) overlap the fraction cannot be reduced. But if you had a common factor X then both the top and bottom could be divided by X to get an equivalent but reducded form of the fraction.
 
  • #3
dmoravec's got it.

Try dividing both top and bottom by small primes -- 2, 3, 5, 7, etc. -- until either the top or bottom is prime, or they share no common factors.

- Warren
 
  • #4
You might try looking at the http://en.wikipedia.org/wiki/Euclidean_algorithm" for finding the greatest common divisor of two numbers.
 
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  • #5
Hey thanks all. That Euclidean algorithm worked like a charm. Fancy.
 

FAQ: Simplify Fractions: Tips and Tricks for Quick and Easy Simplification

1. How do I simplify fractions?

Simplifying fractions involves dividing both the numerator and denominator by their greatest common factor (GCF). This means finding the largest number that evenly divides into both the top and bottom numbers. Once you have found the GCF, divide both numbers by it to simplify the fraction.

2. Can all fractions be simplified?

Yes, all fractions can be simplified as long as the numerator and denominator are both whole numbers. However, some fractions may already be in their simplest form and cannot be further simplified.

3. What is the easiest way to simplify fractions?

The easiest way to simplify fractions is to first find the GCF of the numerator and denominator. This can be done by listing out all the factors of each number and finding the largest one they have in common. Then, simply divide both numbers by the GCF to simplify.

4. Can I use a calculator to simplify fractions?

Yes, most calculators have a simplifying function that can find the GCF and divide the numbers for you. However, it is important to also understand the steps and concepts behind simplifying fractions in case you encounter a fraction that cannot be simplified with a calculator.

5. How can simplifying fractions help in solving math problems?

Simplifying fractions can make working with fractions much easier and more manageable. It can also help in finding equivalent fractions and comparing fractions. In more advanced math, simplifying fractions can also be helpful in solving equations and finding solutions.

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