Algebra Honors (Periods 5 & 6)

Adding & Subtracting Fractions 
The Least Common Denominator 6-4

We know that we can write a fraction in simpler form by dividing its numerator and denominator by the same nonzero number.

and the reverse is true as well

You can write a fraction in a different form by multiplying the numerator and denominator by the same nonzero number.

3/7 = ?/35

You realize that you multiply 7 by 5 to obtain 35 so you would multiply 3 by 5 to obtain the correct number for the numerator.

3/7 = 15/35

the same applies to fractions with variables…

8/3a = ?/18a²

What do you multiply 3a by to obtain 18a²?   6a

so you must multiply both by 6a    

 Complete:

   

You notice that you need to multiply the denominator by (x +1) so you must do the same to the numerator.

When you add or subtract fractions with different denominators, you will find that using the Least Common Denominator (LCD)  will simplify your work

Find the LCD of:

First factor each denominator completely. Factor Integers into primes!

6x - 30 = 6(x - 5)= 2·3(x - 5)

9x - 45 = 9(x - 5) = 3∙3(x - 5)

Form the product of the greatest power of each
(Remember that the LCM is the product of every factor to its greatest power)

2·3²(x - 5) = 18(x - 5)

Therefore the LCD is 18( x – 5)

Re write the following with their LCD

x² - 8x +16 = (x - 4)²

and

x²- 7x + 12 = (x - 4)(x - 3)

the LCD is (x -4)²(x -3)

Now rewrite each fraction using the LCD

 and