Reducing Fractions
When working with fractions, you are usually asked to ‘‘reduce the fraction to lowest terms’’ or to ‘‘write the fraction in lowest terms’’ or to ‘‘reduce the fraction.’’ These phrases mean that the numerator and denominator have no common factors. For example, 2/3 is reduced to lowest terms but 4/6 is not. Reducing fractions is like fraction multiplication in reverse. We will first use the most basic approach to reducing 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 how to find the prime factorization of a number. Next collect the primes
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
primes. Now the fraction is in the form of ‘‘1’’ times another fraction.
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