In this example, you can cross out a pair of 2's and a pair of 3's.īasically, this process tells you that simplifying a fraction boils down to completely factoring the numerator and denominator and then eliminating matching pairs of factors on opposite sides of the fraction bar. If any factor in the numerator has a twin in the denominator, cross those two twin numbers out. Remember, the whole purpose of this exercise was to simplify the fraction 12 30, and you're moments away from accomplishing that goal. (I just wrote the factors from least to greatest.) When you've finally got the numerator and denominator factored, rewrite the fraction using those strings of factors. 5, and you'll get the prime factorization for 30: 2.10 = 30, but 10 is not a prime number.Now it's time to factor 30 into prime numbers. That's because (according to a theorem called the Fundamental Theorem of Algebra) every number has its own, unique prime 6 in your attempt to get the prime factorization of 12, when you further factored the 6, you'd have gotten 2.Since all of those numbers are prime, that's the prime factorization you're looking for. However, that's not a prime factorization because 4 is a composite number. For example, here are two numbers that multiply to get 12 (the numerator): 4 This means breaking down each number into a product and then factoring those numbers until all you're left with are prime numbers. Rewrite the numerator and denominator as a product of prime factors. Now, I want to show you why that works.Ĭonsider the fraction 12 30. Back then, I told you that the best way to reduce a fraction was to divide both its numerator and denominator by any common factors. However, since rational expressions are just fractions, one skill precedes learning those operationsyou need to be able to reduce those fractions also.īefore I show you how to simplify fractions containing polynomials, though, I want to revisit the process I described for simplifying numeric fractions. The plan of action for this section should be familiar once again, with the introduction of a new concept, you'll learn how to add, subtract, multiply, and divide the new element.
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