## adding and subtracting fractions with unlike denominators

Question

adding and subtracting fractions with unlike denominators

0

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:

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.

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)