2/5n=3/10n-3/5

Question

Solving fractional equations

 

Answer 1

Hi Abby,

 

2n    =    3n      -   3

---          ---         ---

5            10          5

 

To make all denominators the same in this equation, ask yourself "what times 5 equals 10?" Two is the answer. Multiply both of the fractions with a denominator of 5 by 2 / 2. When you do this, you will get:

 

4n    =    3n    -     6

---          ----        ---

10           10         10

 

 

Now you can combine terms. Move the 3n / 10 fraction to the left side by subtracting it from both sides. When you do that, you will get

 

(1)n    =    (-)6

-----          -----

10            10

 

Since the fractions have the same denominator, the numerators are equal. When you set 1n = -6, you realize that n = -6.

 

To be sure, you can cross multiply:

 

1n * 10 = -6 * 10

10n      = -60

 

Divide both sides by 10.

n = -6.

 

 

Answer 2

(2)/(5n) = (3)/(10n) - 3/5

 

Multiply both sides by 10n (the lcd) to obtain:

 

4  = 3 - 6n.  So, 1 = -6n.  Therefore, n = -1/6.