simplifying fractions

When working with fractions, we are usually asked to “reduce the fraction to
lowest terms” or to “write the fraction in lowest terms” or to “simplify the fraction.”
These phrases mean that the numerator and denominator have no common
factors (other than 1). For example, 2/3 is in written in lowest terms but 4/6 is not
because 2 is a factor of both 4 and 6. Simplifying fractions is like fraction multiplication
in reverse. For now, we will use the most basic approach to simplifying
fractions. In the next section, we will learn a quicker method.
First write the numerator and denominator as a product of prime numbers.
(Refer to the Appendix if you need to review finding the prime factorization of
a number.) Next collect the prime numbers common to both the numerator and
denominator (if any) at beginning of each fraction. Split each fraction into two
fractions, the first with the common prime numbers. This puts the fraction in
the form of “1” times another fraction. This might seem like unnecessary work
(actually, it is), but it will drive home the point that the factors that are common
in the numerator and denominator form the number 1. Thinking of simplifying
fractions in this way can help you avoid common fraction errors later in algebra.