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.
Examples
Practice
Solutions
Fortunately there is a less tedious method for
reducing fractions to their lowest terms. Find the largest number that divides both the numerator and the denominator. This number is
called the greatest common divisor (GCD). Factor the GCD from the numerator and denominator and
rewrite the fraction. In
the previous examples and practice problems, the product of the common primes was the GCD.
Practice
Solutions
Sometimes the greatest common divisor
is not obvious. In these cases you might find it easier to reduce the fraction in several steps.
Practice
Solutions
Sumber
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