Addition and Subtraction of fractions

Addition and Subtraction of fractions - In order to add like fractions or subtract like fractions, we add or subtract their numerators and retain the common denominator.
For example:   5 + 2 = 7
                      8    8    8

Now to add unlike fractions or subtract unlike fractions, we follow the following steps:
•    Obtain the fractions and their denominators.
•    Find the Least Common Multiple (LCM) of the denominators.
•    Convert each fraction into an equivalent fraction having its denominator equal to the LCM obtained in previous step.
•    Add or subtract like fractions obtained.
   
For example, 7 + 2
                   10  15
LCM of 10 and 15 is (5 X 2 X 3) = 30

So, we convert the given fractions into equivalent fractions with denominator at or 30.

We have, 7 = 7 X 3 = 21       and 2 = 2 X 2 = 4
             10   10 X 3   30            15   15 X 2   30

7 + 2 = 21 + 4 = 21 +4 = 25 = 5
10   15   30   30      30      30     6

Example 2: Simplify-
15 – 11
16    12
LCM of 16 and 12 = (4 X 4 X 3) = 48
15  - 11    = 15 X 3 – 11 X 4  = 45 – 44  = 1
16     12       16 X 3    12 X 4     48    48    48

Try the following yourself:
1. Add:   +
(Answer: 1)
2. Add:  +
      (Answer:)
3.  Subtract:  -
(Answer:)
4. Subtract:  -
(Answer:)

Multiplication and Division of fractions

Multiplication of fractions - To multiply fraction we use the following formula:
Product of two fractions = Product of their numerators
                                      Product of their denominators

For example:   3 X 4   = 3 X 4 = 12
                      7   5       7 X 5    35
Try yourself:
1. Multiply:  x
(Answer:  )
2. Multiply:  x

(Answer:)
Division of fractions – The division of a/b by a non-zero fraction c/d is defined as the product of a/b with the multiplicative inverse or reciprocal of c/d. 
a ÷ c =  a x d
b     d     b   c
For example: 3 ÷ 5    = 3 x 9 = 3 x 9 = 27
                    5     9       5   5     5 x 5    25
Try yourself:
1. Divide:  ÷
(Answer: 1)
2. Divide:  ÷
(Answer:)

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Reference Links:

• http://www.aaamath.com/fra57ax2.htm
• http://www.aaamath.com/fra57bx2.htm
• http://www.youtube.com/watch?v=MEo0rSZ4O3w
• http://www.youtube.com/watch?v=T8Lo_cOW0As&feature=related
• http://en.wikipedia.org/wiki/Least_common_multiple
• http://www.aaamath.com/fra66mx2.htm
• http://www.youtube.com/watch?v=fCzBRpqvA6k&feature=related
• http://www.aaamath.com/fra66px2.htm