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How Common
Finding Common Denominators Least Common Multiple Method

 
 The way that we used to find a common denominator 
 on the last page always works. 
 You can use it any time you need to find a common denominator. 
 But sometimes when you use it, 
 the numbers you get are really, really big. 
 
 So here's a second way:
 
 Add the same numbers as we did on the last page:
 

 
 
 STEP 1: 
 Make up a times table for each denominator
 up to the higher denominator.
 

For 8

 For 6
1 x 8 =   8 1 x 6 =   6
2 x 8 = 16 2 x 6 = 12
3 x 8 = 24 3 x 6 = 18
4 x 8 = 32 4 x 6 = 24
5 x 8 = 40 5 x 6 = 30
6 x 8 = 48 6 x 6 = 36
7 x 8 = 56 7 x 6 = 42
8 x 8 = 64 8 x 6 = 48
 
 STEP 2: 
 Find the smallest product number that shows up on both lists:
 
For 8 For 6
1 x 8 =   8 1 x 6 =   6
2 x 8 = 16 2 x 6 = 12
3 x 8 = 24 3 x 6 = 18
4 x 8 = 32 4 x 6 = 24
5 x 8 = 40 5 x 6 = 30
6 x 8 = 48 6 x 6 = 36
7 x 8 = 56 7 x 6 = 42
8 x 8 = 64 8 x 6 = 48
 
 STEP 3: 
 Use the "other" number from the times table 
 to create fractions equal to 1.
 (That is, the 3 from the For 8 table
 and the 4 from the For 6 table.)
 
For 8 For 6
1 x 8 =   8 1 x 6 =   6
2 x 8 = 16 2 x 6 = 12
3 x 8 = 24 3 x 6 = 18
4 x 8 = 32 4 x 6 = 24
5 x 8 = 40 5 x 6 = 30
6 x 8 = 48 6 x 6 = 36
7 x 8 = 56 7 x 6 = 42
8 x 8 = 64 8 x 6 = 48

 
 STEP 4: 
 Multiply the fractions in the problem by these new fractions
 so that the denominators are the same ...
 

 
 
 STEP 5: 
 Now we have a common denominator, so we can add.
 

 
 STEP 6: 
 Simplify the answer if possible:
 

 
 There are no same factors on the top and the bottom,
 so the fraction can not be simplified.
 
 This method works with subtraction too!
 

   copyright 2005 Bruce Kirkpatrick
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