SOLUTION: can you explain how to add and subtract a variable fractions.. in many ways 1.) 3/x + 5/y = 2.)y/20 - 10/x = 3.)(x/20 + y/50) - 30/y

 +   

3 is the "upper left"
x is the "lower left"
5 is the "upper right"
y is the "lower right"

Rule:

"(Upper left times lower right) plus (upper right times lower left) all over
(bottom times bottom)"

Results:



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Same for subtracting, except use "minus"

 -   

y is the "upper left"
20 is the "lower left"
10 is the "upper right"
x is the "lower right"

Rule:

"(Upper left times lower right) minus (upper right times lower left) all over
(bottom times bottom)"

Results:



Write 10*20 as 200:



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Or this second way

 + 
 
Get the least common denominator of xy

1. Divide the first denominator x into the least common
denominator xy and get y

2. Multiply the first fraction by unit fraction 

· + 

3. Divide the second denominator y into the least common 
denominator xy and get x

4. Multiply second fraction by unit fraction 

· + ·

5. Multiply tops and bottoms in both terms

 + 

6. Since the denominators are the same, (xy and yx are the same),
   add the numerators and put them over the common denominator 



Same for subtracting, except use - for +

 - 
 
Get the least common denominator of 20x

1. Divide the first denominator 20 into the least common
denominator 20x and get x

2. Multiply the first fraction by unit fraction 

· - 

3. Divide the second denominator x into the least common 
denominator 20x and get 20

4. Multiply second fraction by unit fraction 

· - ·

5. Multiply tops and bottoms in both terms

 - 

6. Since the denominators are the same,
   subtract the numerators and put them over the common denominator 



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Here's a third way to do the first one:

 + 

1. Get the least common denominator, xy

2. Multiply both fractions by the unit fraction 

· + ·

3. Cancel left denominators into right numerators in each:

· + ·

 + 

4. Since the denominators are the same, add the numerators and put them 
   over the common denominator 


 
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I'll do the third one by the second method:

( + ) - 

Remove the parentheses first

 +  - 

Get the least common denominator of 100y

1. Divide the first denominator 20 into the least common
denominator 100y and get 5y

2. Multiply the first fraction by unit fraction 

· +  - 

3. Divide the second denominator 50 into the least common 
denominator 100y and get 2y

4. Multiply second fraction by unit fraction 

· + · - 

5. Divide the third denominator y into the least common 
denominator 100y and get 100

6. Multiply third fraction by unit fraction 

· + · - ·

7. Multiply tops and bottoms in all three terms

 +  - 

8. Since the denominators are the same, combine the numerators and put 
   them over the common denominator 

  


Edwin