The Visual / Auditory / Symbolic / Kinesthetic Approach to Algebra

Algebraic Division

      Algebraic division has the same algorithm, procedure, as regular division.


1st:Use a blank rectangular sheet of paper to separate the storage region from the display area and to create a border for the rectangular area.
2nd:Represent the divisor vertically in storage on the left edge of the display area.
3rd: Represent the dividend in the display area in descending order beginning with the upper left corner.
4th:Arrange, if possible, the dividend in IDENTICAL rows in the display area. Matching one row per vertical divisor tile leaves remainders extra in the storage area.
5th:Once a single rectangular arrangement of tiles (extra remainder tiles excluded) is created, represent the appropriate quotient horizontally in the storage area as dictated by the dividend.
6th: If a single rectangular arrangement of tiles is not possible, add zeros as needed to fill the required area.
7th:Read the quotient and the remainder.

      The work and answer for each of these problems is shown below and individually through the arrow.

ex. 1. Divide 4x-12 by 4. ex. 5. Divide (x - 4x + 3) / (x-1)
ex. 2. Divide (x+x) x ex. 6. Divide x - x - 6 by x-3.
ex. 3. Divide (2x+6x-2x+1) / (2x) ex. 7.Divide x + 7x - 11 by x-5.
ex. 4.Divide (x + 4x + 3) / (x+3)

, Unit 18   © 2008, A. Azzolino