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Reducing fractions to lowest terms

To learn how to simplify fractions you can use a calculator. There are many only calculators. You only have to enter your numerator and denominator into the boxes of the reduce fractions calculator and you will get the simplest form of your fraction.

The simplifying fractions calculator will divide both the numerator and the denominator by their Greatest Common Factor (GCF) and reduce it to lowest term. It so simple as that. You can also try it on large fractions, improper fractions and mixed fractions.

It so easy that you can learn how to reduce fractions without a calculator. We will show you how!

Rules for reducing fractions

Now we will show you the basic rules for simplifying fractions. Simplifying or reducing fractions means making the fraction as simple as possible. Why say 3/9 when you mean 1/3? How do I reduce a fraction? There are two methods to simplify a fraction.

First method for reducing fractions: try dividing both the numerator and the denominator of the fraction until you can't go any further. So 6/12 becomes 2/4 and 2/4 becomes 1/2.

When using the second method for simplifying fractions we only use one step by dividing both the numerator and the denominator by the greatest common factor. So 8/12 becomes 2/3.

Greatest common factor to reduce fractions

So before you can start with exercises on reducing fractions we will learn how to find the greatest common factor. When you now how to find the greatest common factor than simplifying fractions becomes very easy.

The greatest common factor or highest common factor of integers is the largest positive integer by which any of the numbers can be divided to yield another integer. To find the greatest common factor you have to list the factors of each of the numbers in a set, then locate the largest integer that is a factor for all of them. This is the greatest common factor. What is the greatest common factor of 24 and 40? The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. The greatest common factor is 8.

Easy way to find greatest common factor

Normally you will search for all the factors of both numbers. This is not necessary

Example large method for reducing fractions:
You can evenly divide 8 by 1, 2, 4 and 8.
You can evenly divide 32 by 1, 2, 4, 8, 16 and 32.
Therefore the largest common factor of both numbers is 8.

Now we will learn an easy way to find the greatest common factor. Start with the biggest number (32 in our example). Now find its biggest factor that is smaller or equal to the other number. To first factor you will find is 16, but that is to big. The second factor you will find is 8. When you check you will see that 8 is a factor of 8. That is great. You have already find the greatest common factor.

Lets try another exercise. GCF of 12 and 20. The biggest factor of 20 that is smaller than 12 gives you 10. But 10 is not a factor of 12.
The next factor is 5, but 5 is not a factor of 12
Now you will find 4 and 4 is a factor of 12 and becomes the GCF.

improper fractions

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