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Reducing Fractions

Reducing Fractions. By: Greg Stark EC&I 831. What is meant by reducing fractions?. To reduce a fraction means that we find an equivalent fraction that has no common factors in the numerator and the denominator

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Reducing Fractions

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  1. Reducing Fractions By: Greg Stark EC&I 831

  2. What is meant by reducing fractions? • To reduce a fraction means that we find an equivalent fraction that has no common factors in the numerator and the denominator • To find this equivalent fraction, we divide both the numerator and the denominator by their GCF Represents the number of parts of a whole we have. Numerator -------------------- Denominator Represents the number of parts into which the whole has been divided

  3. For example: 1 1 1 1 X 2 --- X 2 X 2 ---- X 2 X 2 --- X 2 16 32 1 2 4 8 8 16 16 32 1 2 2 4 X 2 --- X 2 = = = = =

  4. How do we find the GCF? We list the factors of the numerator and the denominator: 16 : 1, 2, 4, 8, 16 16 32 : 32 1, 2, 4, 8, 16, 32 The greatest common factor is 16

  5. Divide both the numerator and the denominator by the GCF 16 32 1 2 1 ÷ 16 ---- ÷ 16 = ½ is the equivalent fraction in lowest terms to 16/32

  6. Factoring by primes List the prime factors for the numerator and the denominator: 12 : 2 X 2 X 3 The GCF is 3 12 27 12 27 4 9 12 27 4 9 : 27 3 X 3 X 3 ÷ 3 ---- ÷ 3 = in lowest terms is

  7. Factoring by primes List the prime factors for the numerator and the denominator: 8 : 2 X 2 X 2 The GCF is 2 X 2 = 4 8 12 8 12 2 3 8 12 2 3 : 12 2 X 2 X 3 ÷ 4 ---- ÷ 4 = in lowest terms is

  8. Review: To reduce a fraction to lowest terms • Find the GCF of both the numerator and the denominator by either: • listing the factors of each • prime factorization of each • Divide both the numerator and the denominator by the GCF

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