Blog Entry 4 --- Alessandro C.

Blog Entry 4

My name is Professor Ceccarelli and today we will be learning about how to find the lowest common denominator. The LCD is used to successfully add or subtract two fractions. In our explanation we will use the example:

(5/6) - (2/4) =?

As we can see, the denominators are six and four. Fractions with different denominators cannot be subtracted.

1. The first step is to identify the multiples of each denominator.

Four	4	8	12	16	20	24	28
Six	6	12	18	24	30	36	42

We can see that the lowest common multiple here is ‘12’ so we will use this one for our fractions. Note that even though ‘24’ is represented in both sets, it is not the lowest option.

2. Now, we apply the LCD to both fractions.

(5/6):

To get to 12, we had to multiply 6 by 2 and whatever is done on the bottom is done on the top, so we get the new fraction with the LCD: (10/12)

(2/4):

To get to 12, we had to multiply 4 by 3 and whatever is done on the bottom is done on the top, so we get the new fraction with the LCD: (6/12)

3. We can add the two fractions with LCDs together

When adding together, it is important to remember that the LCD is not subtracted. The denominator stays the same until there is no more equal sign.

(10/12) - (6/12) = (4/12)

4. After subtracting the fractions we can simplify

After the two fractions are combined, the answer can be simplified to be (1/3)!!

-------------------------------------

Now we will do one more example with a variable in order to cover the things to look out for. Here, we also identify the LCD, but do so by looking at the differences in each fractions denominator and making sure it is represented in both fractions.

Lets use:

[2/(x-2)] + [3/x(x-2)]

In this example, (x-2) is in both denominators, but (x) is only in the second one. We take all the elements from both denominators, therefore our LCD is [x(x-2)]. Once again, what is changed on the bottom must be changed on the top. So,

[2x/x(x-2)] + [3/x(x-2)]

Note that the second fraction requires no change, as the LCD was already represented.  Now, we can add the fractions (Once again, LCD stays the same while numerator is added).

Your answer will be: [2x+3/x(x-2)]

Great job! Now you know how to find the LCD and add fractions! Here are a few practice examples. Good luck!

a) (7/3x) + (5/2x)

b) [5/(x^2+2x)] – [2/x(x-2)]

c) [4/(x-2)(x+3)] + [1/(x-1)(x+3)]