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# Math 0300 Notes: Fractions by vLqjRHz

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```									                        FRACTION OPERATIONS

Multiplication: Multiply the tops, Multiply the bottoms, reduce

Division: 1. Flip 2nd fraction over, change to multiplication
2. Multiply the tops, Multiply the bottoms, reduce

Addition & Subtraction: (Look at the bottom number, the denominator)
Type I: Same denominators                     Type II: Different denominators
 Keep bottom number             * Butterfly Method
 Add/Subtract the tops          * Common Denominator Method
 Reduce
Mixed Numbers: Change to improper
Whole Numbers: Change into a fraction by writing it over a ‘1’.

Butterfly: * Bottom Number: Multiply bottoms = new bottom

2       4
+           =
3       5           15

*To get the top number: Cross-multiply
2        4          2        4      2     4    22
+                   +              +     =
3        5          3        5      3    5     15
10                  10       12     10 + 12 = 22 (New Top Number)
Common Denominators:
 Find LCD (same as LCM) of the denominators
2      3       1
+       +        LCM of 3, 4 and 6 =12
3      4       6
 Change all bottoms to the LCD

2   3            1
+   +
3   4            6
+      +
12      12     12
 Figure out what number you multiplied by to change each old denominator
into a 12 and multiply the top by the same number
2 x4 = 8        8
3 x4 = 12      12
Now that you have the same denominators
3  x3 = 9       9
*add the tops, keep the bottoms, reduce
4 x3 = 12      12
8 + 9 + 2 = 15
1 x2 = 2       2                19
+               +                 =
6 x2 = 12     12                12

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