Dividing using Algebra Tiles

To divide by a constant, form equal groups of algebra tiles.

Example 5

Divide «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»4«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»8«/mn»«mi»x«/mi»«mo»+«/mo»«mn»16«/mn»«/mrow»«mn»4«/mn»«/mfrac»«/math».

Represent «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn mathcolor=¨#B94A48¨»4«/mn»«msup mathcolor=¨#B94A48¨»«mi mathcolor=¨#B94A48¨»x«/mi»«mn»2«/mn»«/msup»«mo mathcolor=¨#B94A48¨»-«/mo»«mn mathcolor=¨#B94A48¨»8«/mn»«mi mathcolor=¨#B94A48¨»x«/mi»«mo mathcolor=¨#B94A48¨»+«/mo»«mn mathcolor=¨#B94A48¨»16«/mn»«/math» using algebra tiles.

Split these tiles into 4 equal groups.

The contents of one group represents the quotient.

«math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#B94A48¨»«mrow»«mn»4«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»8«/mn»«mi»x«/mi»«mo»+«/mo»«mn»16«/mn»«/mrow»«mn»4«/mn»«/mfrac»«mo mathcolor=¨#B94A48¨»=«/mo»«msup mathcolor=¨#B94A48¨»«mi mathcolor=¨#B94A48¨»x«/mi»«mn»2«/mn»«/msup»«mo mathcolor=¨#B94A48¨»-«/mo»«mn mathcolor=¨#B94A48¨»2«/mn»«mi mathcolor=¨#B94A48¨»x«/mi»«mo mathcolor=¨#B94A48¨»+«/mo»«mn mathcolor=¨#B94A48¨»4«/mn»«/math»

To divide a polynomial by a monomial, represent the divisor (the monomial in the denominator) as the length of a rectangle. Represent the dividend (the polynomial in the numerator) as the area of that rectangle with length equal to the divisor. This may require some thoughtful arranging of tiles. The width of the rectangle represents the quotient.

Example 6

Divide «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»6«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»3«/mn»«mi»x«/mi»«/mrow»«mrow»«mn»3«/mn»«mi»x«/mi»«/mrow»«/mfrac»«/math».

Represent «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn mathcolor=¨#B94A48¨»3«/mn»«mi mathcolor=¨#B94A48¨»x«/mi»«/math» as the length of a rectangle, using algebra tiles.

Represent «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn mathcolor=¨#B94A48¨»6«/mn»«msup mathcolor=¨#B94A48¨»«mi mathcolor=¨#B94A48¨»x«/mi»«mn»2«/mn»«/msup»«mo mathcolor=¨#B94A48¨»-«/mo»«mn mathcolor=¨#B94A48¨»3«/mn»«mi mathcolor=¨#B94A48¨»x«/mi»«/math» using algebra tiles and arrange them as the area of a rectangle with length «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn mathcolor=¨#B94A48¨»3«/mn»«mi mathcolor=¨#B94A48¨»x«/mi»«/math».

Identify the tiles needed to represent the width. Place those along the left side of the rectangle. This width represents the quotient.

«math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#B94A48¨»«mrow»«mn»6«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»3«/mn»«mi»x«/mi»«/mrow»«mrow»«mn»3«/mn»«mi»x«/mi»«/mrow»«/mfrac»«mo mathcolor=¨#B94A48¨»=«/mo»«mn mathcolor=¨#B94A48¨»2«/mn»«mi mathcolor=¨#B94A48¨»x«/mi»«mo mathcolor=¨#B94A48¨»-«/mo»«mn mathcolor=¨#B94A48¨»1«/mn»«/math»