Reduce A Fraction in Tilted Array Display.
|1st:||Arrange the tiles in IDENTICAL rows (or columns),
if possible. The ARRANGEMENT of tilted and nontilted tiles in EVERY row (or every column) must be
IDENTICAL. This will factor out a constant.|
|2nd:||Remove ALL BUT ONE row (or column) from the display
area to represent the entire reduced fraction.|
|3rd:||Repeat steps 1 and 2 on the new display of tiles to see if the
reduced fraction may also be reduced.|
Examine the work above on reducing 4/8. Placing tiles in rows and columns
FACTORS the denominator into a factor pair, (the number of rows) x (the number of columns). Notice that in
the box with 8 tiles, the tiles are in two rows and 4 column (8 = 2 x 4). Because the 2 rows of tiles can be
made, 2 is a factor of the denominator. Because 2 IDENTICAL rows are possible, 2 is a factor of the
numerator. Since 2 is a factor of the numerator and the denominator, the fraction 4/8 is 2/4.
To reduce 2/4, creating 2 identical rows means there is a factor of 2 in the
denominator (because of the rows) and in the numerator (because of the identical). The fraction 2/4 may be
reduced to 1/2.
Reduce: j. 24/30, k. (8x)/(10x), l. (2x² -2x -12)/(4x+8)
To reduce 24/30, creating 3 identical rows means there is a factor of 3 in the
denominator (because of the rows) and in the numerator (because of the identical). The fraction 24/30 may be
reduced to 8/10. To reduce 8/10, creating 2 identical rows means there is a factor of 2 in the denominator
(because of the rows) and in the numerator (because of the identical). The fraction 8/10 may be reduced to 4/5.
Reduce Fractions in Numerator / Denominator Form
|1st:||Simplify the tiles in the numerator and
denominator display areas.|
|2nd:||Factor the numerator, if possible.|
|3rd:||Factor the denominator, if possible.|
|4th:||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|
THEY DON'T HAVE IN COMMON
AS THE NEW NUMERATOR AND THE NEW DENOMINATOR.
|5th:||Repeat steps 1 and 2 and 3 and 4 as often as needed.|