Q:

# How do you reduce fractions?

A:

### Quick Answer

To reduce or simplify fractions, look for common factors in the numerator (the term on top) and the denominator (the term on the bottom). Divide both terms by the greatest common factor to reduce the fraction to its lowest terms.

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### Full Answer

1. Identify the prime factors in both the numerator and denominator

Break each term down into its prime factors, and write those factors in the numerator and denominator of an equivalent fraction. Consider the example 14/20; breaking this fraction into prime factors results in this equation: 14/20 = 7 x 2 / 2 x 2 x 5.

2. Identify the common factors in the numerator and denominator

Look at the factors in the numerator (2 and 7), and look at the factors in the denominator (2 and 5). The common factor between the numerator and denominator is 2, which means you can reduce both numerator and denominator by a factor of 2.

3. Simplify the fraction by removing common factors

Cross the 2 out in the numerator, and cross one of the 2's out in the denominator. Remember that you can only cross out as many 2's (or other factors) as there are in both the numerator and denominator. The example from Step 2 (7 x 2 / 2 x 2 x 5) now reduces to 7 / 2 x 5. Multiply out to find the solution, which is 7/10.

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