Fractions are mostly used together with integers. So, we introduce boards in pairs.
Examples
In each case you create a fraction board by dividing all whole numbers on the integer board
by their least common multiple. If you use only one counter per square, the total is
represented as a sum of unit fractions. (This way of representing fractions was used in
ancient Egypt.) But you may stack more tokens on one square to represent bigger numerators.
Examples
1/6 + 1/3 = 1/2
1/6 + 1/6 + 1/5 + 1/15 + 1/15 + 1/30 = 7/10
1 + 1/4 + 1/6 + 1/6 + 1/6 + 1/10 + 1/10 + 1/15 + 1/15 + 1/30 = 127/60
The most important fact is that the rules of regrouping are the same on an integer
board and its corresponding fraction board. So for example, if you want to compute
2/5  1/3, you may compute instead 24  20 = 4 and get 1/15 as the answer to the original
problem.
Using the fraction board...
1/5 + 1/5 = 1/3 + 1/15 

1/3  1/3 = 0 
Using the integer board...
12 + 12 = 20 + 4 

20  20 = 0 
After regrouping, the integer board holds 4. On the fraction board, this corresponds to the answer 1/15.
Other Examples
2/15 + 1/30
Using the fraction board...
1/30 + 1/15 = 1/10 

1/15 + 1/10 = 1/6 
Using the integer board...
After regrouping, the integer board holds 5. On the fraction board, this corresponds to the answer 1/6.
1/6  1/10
Using the fraction board...
1/6 = 1/10 + 1/15 

1/10  1/10 = 0 
Using the integer board...
After regrouping, the integer board holds 2. On the fraction board, this corresponds to the answer 1/15.
1/2 + 1/15  4/10
Using the fraction board...
1/10 + 1/10 + 1/10 + 1/10 = 1/3 + 1/15 

1/15  1/15 = 0 
1/2 = 1/6 + 1/3 

1/3  1/3 = 0 
Using the integer board...
6 + 6 + 6 + 6 = 20 + 4 

4  4 = 0 
After regrouping, the integer board holds 10. On the fraction board, this corresponds to the answer 1/6.
Webpage Maintained by Owen Ramsey
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