Addition
A Super Shortcut For Addition and Subtraction
Mixed Numbers
Multiplication
Division
Bottom
To Add and Subtract Fractions your denominators must
BE the SAME
and
STAY the SAME
Ex: 3 + 2 =
4
5
3 = 15
2 = 8
4 20
5 20
15 + 8 = 23
20 20 20
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
+ 2 = 15
+ 8 = 23
4 5
20
20
This method also works for subtraction
Ex: 3 - 1 = 24 - 5 = 19
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 + 8 = 6 23
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 - 16 = 4 -1 = 3 19
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.
1. You cannot multiply mixed numbers.
2. You must first write mixed numbers as improper fractions.
Ex: 3 1 x 2 1 = 10 x 11 = 110 = 22 = 7 1
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.
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