Q:

# What are some tips for finding fractions in the lowest terms?

A:

A long but effective way to reduce a fraction to its lowest terms is to write out lists of all factors of the numerator and the denominator, then identify common factors other than 1. After identifying the common factors, divide the numerator and denominator by the lowest common factor, then repeat the process until the only common factor remaining is 1. A faster method is finding the greatest common factor.

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To use the slower method, begin by making two separate lists of all factors for the numerator and the denominator. For the fraction 24/36, for example, write the list "1, 2, 3, 4, 6, 8, 12, 24" for the numerator and "1, 2, 3, 4, 6, 9, 12, 18, 36" for the denominator. Identify that, other than 1, the numerator and denominator share the factors of 2, 3, 4, 6 and 12. Dividing the numerator and denominator by 2, the lowest common factor, simplifies the fraction to 12/18.

Next, write down the factor list "1, 2, 3, 4, 6, 12" for the numerator and "1, 2, 3, 6, 9, 18" for the denominator.

Dividing the numerator and denominator by 2 yields 6/9. The factor lists for this fraction are "1, 2, 3, 6" and "1, 3, 9." The lowest common factor is now 3, and dividing by this number gives the final simplified fraction 2/3.

The aforementioned method is helpful for identifying several fractions that are also equivalent to the original fraction, but it is not the quickest way to get a fraction in its lowest terms. A quicker method is to look at the two original factor lists and note that 12 is the greatest common factor. Dividing the numerator and denominator by 12 yields 2/3.

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