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Three methods of reducing a fraction

When you simplify or reduce a fraction you are making the fraction as simple as possible. For instance, when 8/16 is reduced it becomes 1/2. Think of it this way,1/2 is easier, or more simple to work with, compared to 8/16
Let’s look at three methods for reducing a fraction

Method #1: Finding Lowest Common Factors
For example:

Ex. 1 Reduce15/18
  • Factor each term:
  • The factors of 15 are 1, 3, 5, 
  • The factors of 18 are 1, 2, 3, 6, 9
  • Notice that 15 and 18 have only one factor in common other than one.
  • Divide the fraction by the lowest common factor, 3. 
  • 15 ÷ 3/18 ÷ 3 = 5/6

Is the fraction simplified? Let’s see
  • The factors of 5 are 1, 5, (prime)
  • The factors of 6 are 1, 2, 3, 6

They do not have any common factors other than one, therefore the fraction is simplified

Ex. 2 Reduce 18/24
  • The factors of 18 are 1, 2, 3, 6, 9
  • The factors of 24 are 1, 2, 3, 4, 6, 8.12
  • Notice that 18 and 24 have the lowest common factor, 2. Divide the numerator and denominator by 2.
18÷2/24÷2 = 9/12
 
Is the fraction simplified? Let’s see….
  • The factors of 9 are 1, 3, 9
  • The factors of 12 are 1, 3, 4, 6, 12
  • The lowest common factor is 3.
9÷3/12÷3 = ¾

There are no more common factors therefore the fraction is reduced 
Method #2: Using the Greatest Common Factor (GCF)
Ex. 3 Reduce  18/24
  • The factors of 18 are 1, 2, 3, 6, 9, 18
  • The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
  • The Greatest Common Factor is 6
  • Divide the fraction by the greatest common factor
18 ÷ 6/24 ÷ 6 = 3/4

Method #3: Divide the Fraction by the Prime Factors

Simplify 15/18
  • The prime factors of 15 are 3 x 5.
  • The prime factors of 18 are 2 x 3 x 3
  • Remove 3 because it is common in the numerator and denominator

3x/2x3x3