6.6 NORMAL PATH simplifying algebraic fractions
Theory
Simplifying algebraic fractions
Two-fifth is an example of a fraction. The 2 is called the numerator and the 5 is called the denominator.
You've already learned how to simplify fractions with numbers only. For example simplifying three-sixth: Divide the numerator and denominator by 3. You will get one-second.
The same works with letters, you always have to divide the numerator and the denominator with the same number and/or letter. Look at the example below.
Adding fractions with a common denominator.
You have already learned that you may add and subtract fractions with a common denominator. This means that the fractions must have the same denominator before you can add or subtract them.
Two fractions with a common denominator:
Two fractions without a common denominator
You can always make denominators the same by multiplying the numerator and the denominator of the fractions with the same number. You only need to do this if you have fractions without a common denominator. You need to do exactly the same with fractions with letters, this will be shown in the example.
Example
Simplifying algebraic fractions
The same as with fractions with only numbers, you can simplify fractions with letters. You may only simplify those fractions by dividing the numerator AND the denominator by the SAME letter.
Simplify
Remember: negative divided by negative equals positive.
We can divide everything by 2 and by w.
You may also divide everything by 2w at once.
Adding fractions with a common denominator
Adding fractions with a common denominator and with letters works exactly the same as with fractions with only numbers. The only difference is that there are letters in your fraction. An example is shown underneath.
We can see that the denominators in this example are the same, they are both 9a. The only think that we need to take in mind is that we are only allowed to add like terms. 4b and 1 are non like terms so, we may not add them. We may put them together in one numerator, as long as we don't add them.
Addin fractions without a common denominator
It is also possible that you get fractions without a common denominator but with letters. Again, you need to do exactly the same as with numbers only, you need to make the denominators the same in order to subtract or add the fractions. You can make them the same with multiplication.
Multiply the numerator and the denominator of the same fraction with the same number in order to make the denominators the same.
Reminder: 3 . 3 = 32 , x . x = x2 so, h . h = h2
You may now add the fractions because the denominators are the same.
You may only add like terms!
Always check if you can simplify your answers any further.
Exercises
Simplify
