Fraction Help Page

BE the SAME
and
STAY the SAME

Ex:        3 + 2 =
4    5

3  =  15                                           2 8
4      20                                            5    20

15 = 23
20    20    20

A Super Shortcut:

Using this concept, there is a shortcut
(my students call this the "Superman" method, after "Up, up, and Away."

Ex:        3 + 2 =
4    5

1.  Multiply "Up" [multiply 5 x 3, up and across the addition sign]
2.  Multiply "Up" [multiply 4 x 2, up and across the addition sign]
3.  Multiply "Away" [Multiply 4 x 5 across the denominator]

Write your results to the right of the equal sign.

Ex:        3 + 215 + 823
4    5        20         20

This method also works for subtraction

Ex:        3 - 124519

5    8        40         40

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Mixed Numbers

To use this for mixed numbers, you have some choices.  For addition, add the whole numbers together first.

Ex:   1   3  +  5   2 =   6   15 + 86   23

4             5              20               20

For subtraction, you might be able to subtract the whole numbers, but you may find that you cannot subtract the numerators (you might have to borrow.)  This will still work, but you must be careful.

Ex:   6   1  -  2   4 =   4   15 - 164    -1  =  3  19

4            5               20                20           20

Note that 15 - 16 is negative one.  To resolve it, subtract 1 from 4 (to get 3).  Replace the 1 with 20/20 and subtract 19.  Note that this is the same as subtracting 20 - 1.

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Multiplication

1.  You cannot multiply mixed numbers.
2.  You must first write mixed numbers as improper fractions.

Ex:   3   1  x  2   1 =    10 x 11110 = 227 1

3            5        3      5       15      3           3

There are shortcuts available for the multiplication (5 divides into 10 twice), but if you are uncomfortable with them, and can calculate competently otherwise, you do not need to cancel.

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Division

1.  You cannot divide mixed numbers.
2.  You must first write mixed numbers as improper fractions.

Ex:    2/3
3/4

To simplify, multiply numerator and denominator by 4/3  (remember:  3/4 x 4/3 = 1).  This will give you:

2/3  x   4/3  =  2/3 x 4/3 8/9 = 8/9
3/4      4/3         12/12          1

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