Pre Algebra (Period 2 & 4)

Adding & Subtracting Fractions 5-3

(positive only)

1) Check for a common denominator

2) If you don't have one, use the LCM as the LCD (least common denominator)

3) Use equivalent fractions to restate to the common denominator

4) When subtracting, be sure to BORROW IF YOU NEED TO!



Adding or subtracting VARIABLES:

If the variable is just in the numerator,
just follow the normal method of finding a common denominator

EXAMPLE:
x/2 + 3x/5 
The common denominator is 10

(5)x/10 + 3x(2)/10      
  (
5x + 6x)/ 
10    = 11x/10  




If the variable is in the denominator, but they are the same variables, just add/subtract normally because you have a common denominator

EXAMPLE:
3/y + 7/y = 10
/y  

If in the denominator, but the denominators are not the same, multiply the two denominators together and use equivalent fractions just as you would do with number denominators.


This time you will have to multiply by a variable.

EXAMPLE:
3/y - 7/10 
 
The LCD is 10y:

[(10)3 - (y) 7 ]/
(10) y   =

(30 - 7y)/10y

 
There's also a trick to this that I showed you in class!
You simply multiply the 2nd denominator by the 1st numerator.
Then multiply the 1st denominator by the 2nd numerator.
The denominator is the product of both denominators.
Only works if there are just 2 terms!!!

NEGATIVE FRACTIONS


1) Double check any subtractions just as you would for integer problems

2) Place the bigger fraction on the top (no matter the sign)

3) Restate to common denominators if needed

4) Borrow if the fraction below is larger than the fraction above

5) Make sure your answers have consistent signs - In other words, if you have a negative fraction, make sure your whole number part is also negative

OR

1) You can simply make all mixed numbers into improper fractions first

2) Find a common denominator

3) Use integer rules with the numerators

4) Restate back into mixed numbers if required

EXAMPLE using both methods:


5 2/3 - 10 1/4


KEEP THEM AS MIXED NUMBERS:
First of all, you know the final answer will be NEGATIVE so make sure it is!
STACK THEM!! With the WINNER on TOP

10 1/4
5 2/3


Find a common denominator:

10 3/12

5 8/12


Borrow because the bottom number is bigger than the top number

9 15/12

5 8/12

Use integer rules to add or subtract:

-4 7/12


Check: If so, you've got the answer:
(if not, you needed to borrow and you forgot to!)
-4 7/12