Adding and Subtracting Unlike Fractions

We learned in the previous section about adding and subtracting fractions when we were already given a common denominator. The process is very simple when there is a common denominator because you just have to add/subtract the top numbers and then simplify. You keep you bottom number the same.

Now when you have fractions that don't have common denominators, before you can add/subtract you must first find a common denominator. A common denominator is just like find the least common multiple of two numbers. We want to find a number that both denominators will divide into evenly. Keep in mind the least common denominator (LCD) can be no smaller than the largest denominator. For example:

1/3 + 5/6 The LCD can be no smaller that 6 because is the largest denominator. Fortunately for us the LCD is 6. We will talk more about this in a minute.

Once you have found the LCD, you then write an equivalent fraction using the LCD. Remember last chapter when we wrote equivalent fractions we would just multiply the top and bottom number by the same number of our choosing? We do the same thing now except we don't get to choose any random number. We have to use a very specific number.

Here is how we put it all together:

1/3 + 5/6 - First we find the common denominator which is six. Then we rewrite the problem using the common denominator.

?/6 + ?/6 - Here is where the equivalent fraction thought comes into play. We need to find out what times 3 gives us the LCD of 6. And we know that it is 2. So, if we multiply the bottom by 2, what do we have to do to the top? That's right, multiply it by 2. The second fraction already has the LCD so the top number stays the same.

2/6 + 5/6 = 7/6=11/6 (this is one and one sixth, this how mixed numbers will look)

Here is another example:

5/9 + 1/6 = 10/18 + 3/18 = 13/18

Remember if you are dealing with mixed numbers it is easier to change them into improper fractions before finding a common denominator. Make sure you simplify if at all possible. Finally, watch you signs when adding and subtracting with positive and negative numbers.

Let me know if you have any questions.