Question

How do the gcf and the lcm help you when multiplying and adding or subracting fractions

Answer 1

Explanation:

GCF: the greatest common factor of numerator and denominator is a factor that can be removed to reduce the fraction.

  Example

The numerator and denominator of 6/8 have GCF of 2:

  6/8 = (2·3)/(2·4)

The fraction can be reduced by canceling those factors.

  (2·3)/(2·4) = (2/2)·(3/4) = 1·(3/4) = 3/4

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LCM: the least common multiple of the denominators is suitable as a common denominator. Addition and subtraction are easily performed on the numerators when the denominator is common.

  Example

The fractions 2/3 and 1/5 can be added using a common denominator of LCM(3, 5) = 15.

  2/3 + 1/5 = 10/15 + 3/15 = (10+3)/15 = 13/15