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

3. 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 Numerator -------------------- Denominator Represents the number of parts into which the whole has been divided Represents the number of parts of a whole we have.

4. For example: 1212 4848 2424 8 16 32 = = == X 2 ---- X 2 --- X 2 --- X 2 --- X 2 16 32 1212 =

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

6. Divide both the numerator and the denominator by the GCF 16 32 ÷ 16 ---- ÷ 16 = 1212 ½ is the equivalent fraction in lowest terms to 16/32

7. Factoring by primes 12 27 12 27 3:2X2X : List the prime factors for the numerator and the denominator: 33X3X The GCF is 3 12 27 ÷ 3 ---- ÷ 3 = 4949 in lowest terms is 12 27 4949

8. Factoring by primes 8 12 8 2:2X2X : List the prime factors for the numerator and the denominator: 32X2X The GCF is 2 X 2 = 4 8 12 ÷ 4 ---- ÷ 4 = 2323 in lowest terms is 8 12 2323

9. Review: To reduce a fraction to lowest terms 1.Find the GCF of both the numerator and the denominator by either: 1.listing the factors of each 2.prime factorization of each 2.Divide both the numerator and the denominator by the GCF