Section 1.2 Fractions Review 17 The reason the fundamental property works is that c c = 1. a · c b · c = a b · c c = a b · 1 = a b ���������������������� Simplifying Fractions Step 1: Write the numerator and denominator with their prime factorizations. Step 2: Divide the numerator and denominator by their common factors. Step 3: Multiply the remaining factors. �� ������������������������ ������������������ Simplify each fraction. 3a. 28 30 3b. 144 99 3c. 116,000,000 309,000,000 28 30 Solutions 3a. = 2 · 2 · 7 2 · 3 · 5 = 2 · 2 · 7 2 · 3 · 5 = 14 15 Write the prime factorization of 28 and 30. Divide out the common factor of 2. Multiply the remaining factors. ���������� It is not necessary to write the prime factorization of the numerator and denominator of a fraction to simplify it. For instance, observe that both 28 and 30 are divisible by 2. So, we can divide them each by 2 to obtain the simplified form of the fraction. 14 28 30 15 = 14 15 144 99 3b. = 2 · 2 · 2 · 2 · 3 · 3 3 · 3 · 11 = 2 · 2 · 2 · 2 · 3 · 3 3 · 3 · 11 Write the prime factorization of 144 and 99. Divide out the common factors. = 16 11 Multiply the remaining factors. 116,000,000 309,000,000 3c. = 116,000,000 4 1,000,000 309,000,000 4 1,000,000 = 116 309 Divide the numerator and denominator by their common factor of 1,000,000. Simplify. Student Check 3 Simplify each fraction. a. 20 32 b. 180 200 c. 104,000 624,000
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