Think mental math for easy to subtract fractions. Think this quick traditional
algorithm for work when not emphasizing prime factorization and creating a common denominator. It is used
in college-level liberal arts courses and by mathematicians, but, not preached in most US high schools.
| Represent Adding the Opposite. |
| 1st: | Use two display area. Let the one on the top (further
from the user) be for the numerator of the difference. Let the one on the bottom (closer to the user) be for
the denominator of the difference. |
| 2nd: | Represent the first numerator in storage on the horizontal
on the top left corner. |
| 3rd: | Represent the first denominator in storage on the vertical
side on the top left corner. |
| 4th: | Represent the OPPOSITE of the second numerator in
storage on the horizontal in the bottom right corner. |
| 5th: | Represent the second denominator in storage on the
vertical of the bottom right corner. |
| 6th: | Represent the product of the two denominators in the
lower display area in a rectangular array of your choice. |
| "Cross Multiply." |
| 7th: | "Cross Multiply" each numerator with the other
denominator placing the results in the numerator display area.
This means, multiply the (numerator) horizontal from the 1st with the (denominator) vertical
from the 2nd, placing the product in the lower left corner.
Then, multiply the (numerator)
horizontal from the 2nd with the (denominator) vertical from the 1st, placing the product in the upper right
corner. |
| Simplify and Reduce. |
| 8th: | Simplify the tiles in the numerator display area. |
| 9th: | Remove tiles for both the numerator and
denominators VERTICAL AND HORIZONTAL storage areas. |
| 10th: | Factor the numerator, if possible. |
| 11th: | Factor the denominator, if possible. |
| 12th: | Use the factors they
DON'T have in common as the new numerator and the new denominator.
Whenever possible, remove a top factor with an identical bottom factor.
TO REDUCE, USE THE
FACTORS
THEY DON'T HAVE IN COMMON
AS THE NEW NUMERATOR AND THE NEW DENOMINATOR. |
|
| 13th: | Repeat steps 9 and 10 and 11 and 12 as often as needed. |
