Monday, February 2, 2009

Writing as a single fraction

Example 1:
If you are asked to add

2/3 + 1/4

you have to first convert them into the same type of fraction i.e. find a new denominator which is the LCM of 3 and 4 => 12
2/3 = 8/12 (you have to multiply the bottom by 4 to go from 3 to 12, so you must do the same with the top)
1/4 = 3/12
So the sum becomes
8/12 + 3/12 = 11/12

Example 2:
The exact same principle applies when you have to add (or write as a single fraction)
5x-1 - 2x + 3
----- -------
4 5

The new denominator will be 20.
You multiply 4 by 5 to get 20, so you must multiply 5x-1 by 5 also giving 5(5x-1) = 25x - 5
Repeat the corresponding operation on the other fraction and then add/subtract like terms.

Example 3:
In question 17 you have to find the LCM of 2x+1 and 2x-1.
This will be (2x+1)(2x-1) and exactly the same principle as in examples 1 and 2 applies.
Remember you don't have to multiply out the denominator (expression on the bottom).

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