How do you use prime factorization to reduce a fraction?
Find the same number that can be divided into both the numerator and denominator.
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To use prime factorization to reduce a fraction, you need to follow these steps:
Step 1: Prime factorize the numerator and denominator of the fraction. Prime factorization involves breaking down a number into its prime factors (numbers that can only be divided by 1 and themselves). For example, if the numerator is 12 and the denominator is 16, their prime factorizations would be 12 = 2^2 * 3 and 16 = 2^4.
Step 2: Identify common factors between the numerator and denominator. Common factors are the prime factors that appear in both the numerator and the denominator. Using the example above, the common factor is 2^2 because both 12 and 16 have a factor of 2 raised to the power of 2.
Step 3: Cancel out the common factors by dividing both the numerator and denominator by the common factors. In this case, divide both 12 and 16 by 2^2. The result would be 12/16 = (2^2 * 3) / (2^2 * 2^2), which simplifies to 3/4.
Step 4: Check if the resulting fraction can be simplified further. If there are still common factors between the numerator and the denominator, repeat steps 2 and 3 until no common factors remain.
Using prime factorization helps in reducing fractions to their simplest form by dividing out the common factors, allowing the fraction to be expressed in its lowest terms.