Question

adding and subtracting fractions with unlike denominators

Answer 1

You must first find a common denominator.
Change the fractions to the common denominator.
Then you add or subtract the fractions.
Finally, you may need to reduce the fraction.

Example 1:

Add

1/5 + 1/3

The least common denominator is 15.

Both denominators must become 15.

1/5 + 1/3 = 3/3 * 1/5 + 5/5 * 1/3 = 3/15 + 5/15 = 8/15

Example 2:

Subtract
3/8 - 1/3

The least common denominator is 24.

3/3 * 3/8 - 8/8 * 1/3 = 9/24 - 8/24 = 1/24

Both in addition and subtraction, you only add or subtract the numerators. The denominator of the answer is the common denominator.

Answer 2

To add or subtract different fractions you need to make both fractions have an L.C.D = lowest common denominator. You can find the LCD by multiplying the denominators of the fractions together. Once you have the LCD you can multiply each fraction by a ratio of one (example = 3/3 ratio = 1 ) to make the denominators equivalent. 

Example problem: 
2/3 + 4/5 = ?
The L.C.D is equal to 15 (from multiplying the denominators 3 and 5 together).
Now you can make the first fraction (2/3) have a denominator of 15 by multiplying it by a ratio of 1 (5/5).  For the second denominator (4/5) multiply it by a ratio of 1 as well (3/3). Now the fractions will be (2/3)(5/5) + (4/5)(3/3) =  10/15 + 12/15 

Because the fractions have the same denominator now you can now add them together and then simplify the fraction to its simplest form. 
10/15 + 12/15 = 22/15 (This fraction cannot be reduced further, it is the final answer)