Simplifying Fractions Is Really Simple, When You Follow The RulesSimplifying fractions is often required when your answer is not in the form required by the assignment. As a matter of fact, most math instructor will demand that you always simplify results. Generally speaking, there are two occasions where simplifying your answer may be necessary.
So let's look at both situations that may require simplifying your answer. Reducing Fractions To Here's the situation. You have added the fractions okay, but your answer may not be showing the lowest equivalent fraction. The easiest way to know for sure that your answer is in its simplified form is to breakdown both the numerator and the denominator into prime numbers. Let's use an easy example so you will get the idea...
Notice that the original answer after adding the fractions is "2/4." To determine if our answer is in its simplest form, we must factor the numerator and the denominator into its prime numbers. Click here for a review of prime numbers. What we are looking for are the prime numbers that are common to both the numerator and the denominator. If we find these common numbers, we can then cancel them out. The results will be a fraction simplified to its lowest equivalent fraction. Since "2" is a common factor in both the numerator and denominator of our example above, it indicates that our answer is not in its simplest form. Therefore, we cancelled out (/)one of the 2's in both the numerator and denominator by dividing by "2". The results is a "simplified fraction" reduced to its lowest form. Here's the Rule for simplifying fractions...
Always keep in mind... Whatever you do to the numerator of a fraction you must also do to the denominator. So if you have to divide the numerator by a number, you must also divide the denominator by the same number. That way you will not change the overall value of the fraction. Let's do a little tougher problem to be sure you've got it...
In this problem, one 2 and one 3 can be found common to both the numerator and the denominator. Notice how we only cancel-out one-for-one! First we divide the numerator and denominator by "2", then divide both the numerator and denominator by "3." So what is left in the numerator is 1 x 1 x 3 = 3, and the denominator is 1 x 2 x 2 x 1 = 4. That leaves use with a reduced fraction equal to 3/4. Got it? GREAT! Now let's look at...
Simplifying
You may remember that an improper fractions is where the numerator has a greater value than that of the denominator. So each time you perform an operation on fractions and your answer ends up as an improper fraction, you will usually need to simplify your answer. The results will be in the form of a mixed number. To convert an improper fraction into a mixed number, just divide the numerator by the denominator. The results will be a whole number part and a fractional part. Here is an example...
As you can see, this is a pretty straightforward operation. But keep in mind that if there is no remainder, the answer is the WHOLE NUMBER only. So as you can see, simplifying fractions is no-big-deal. Just follow the steps above, and simplifying fractions will be like a "walk in the park."
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More Help With Math Fractions...Math Homework Helper - Start Here! Adding Fractions - Same Denominator Adding Fractions - Different Denominators Subtracting Fractions - Same Denominator Subtracting Fractions - Different Denominators Least Common Denominator (LCD) Prime Numbers Chart - A Helpful Tool
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