Pre Algebra Finding Common Denominators Prime Factor Method
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Real Common
Finding Common Denominators Prime Factor Method

 
 GOOD NEWS!!!
 This is our last method for finding common denominators.
 
 Start with something like this ...
 

 
 STEP 1: 
 Break up the denominators into prime factors ...
 

 
 STEP 2: 
 List the denominator (Bottom part) prime factors. 
 Write a number the most times it appears in EITHER fraction.
 This is the common denominator.
 

 2 x 2 x 2 x 3 

 
 STEP 3: 
 Make fractions equal to 1 to multiply each fraction in the problem by. 
 The number you build is made up of the common denominator factors
 that ARE NOT in that denominator.
 
 In the first fraction,
 the denominator is made up of 2 x 3.
 The common denominator 
 is made up of 2 x 2 x 2 x 3
 
 The missing numbers are 2 x 2,
 so that is what we use in our multiplying fraction.
 
 Remember that the multiplying fraction must equal 1.
 That means we use the same thing on the top and bottom
 of the multiplying fraction.
 

 
 You can multiply out the numbers in each fraction first

 if you want to.

 
 Then multiply the fractions ...
 

 
 In the second fraction,
 the denominator is made up of 2 x 2 x 2.
 The common denominator 
 is made up of 2 x 2 x 2 x 3
 
 The missing number is 3,
 so that is what we use in our multiplying fraction.
 
 Remember that the multiplying fraction must equal 1.
 That means we use the same thing on the top and bottom
 of the multiplying fraction.
 

 
 STEP 4: 
 Now we have a common denominator so we can subtract.
 

 
 STEP 5: 
 Simplify if possible ...
 

Since the only thing on the top is a 1,
this one can't be simplified.

 

   copyright 2005 Bruce Kirkpatrick

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