



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 
