The Visual / Auditory / Symbolic / Kinesthetic Approach to Algebra

Reduce Fractions

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. (2x -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
FACTORS 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.




www.termtiles.com, Unit 31   © 2008, A. Azzolino