Enter a number from 1 to 9 in the top
left input box and a row of red disc corresponding
to the number will display.
Enter a number from 1 to 9 in the top
right input box andwhen you click each displayed
disc, a columns of red disc corresponding to the
number will display.
When the disc displayed, the lengths of
the horizontal and
vertical axis, patitioning the array, extended.
When you cick on the axis they may be
dragged to reposition.
When you click on a red disc its color
will change to black and when you click again the
disc change
back to red . (Only click disc filling the bottom
right area of the array.)
The nunbers of disc filling the areas
above the horizontal axis correspond to the
numerators of the equivalent ratios/fractions in the
equation displayed to the right of the array. The
nunbers of disc filling the areas below the
horizontal axis correspond to the denominators of
the equivalent ratios/fractions in the equation
displayed to the right of the array.
The fraction bars may be seen to
corrrespond to the horizontal axis and the equal
sign may be seen to correspond to the vertical axis.
The denominator of the ratio on the
rightside of the equation corresponds to the red and
black disc filling the bottom right area of the
array.
Any black disc in this area will
correspond to the constant of the bottom right
denominator and the remaining red disc in this area
will correspond to the solution for the unknown (X).
Click the Uncover Solution button to see
algebraic solution steps for equation.
Vary number of disc clicked in bottom
right area to change constant and the unknown (X) of
bottom right denominator.
Move vertical axis to multiply
numerators and denominators by a common factor and
not change the equivalent values of the ratios.
Move horizontal axis to increase and
decrease numerators and denominators and thereby change
the equivalent values of the ratios.
Click print to display varying printable
versions of the application.
Click Invert button to see Inverse
Equation
Click top roll of red disc to re-display
complete array.
Click disc again to display black disc
corresponding to constant.
In the inverse equation, the numerator
of the first ratio is the inverse or reciprocal of
the previous numerator. This numerator corresponds
to the fraction: 1 divided by the total number of
disc filling the top left area of the array.
The cross product of the numerators and
denominators now corresponds to the number of
red disc filling the bottom right area of the array.
The product of any 2 non adjacent areas
of the array now correspond to the solution of the
unknown (X).
Any factors of the number of red disc
filling the botton right area of the array may be
entered as the denominator of the ratio on the left
side of the equation and the numerator of the ratio
on the right side of the equation.
Left click on these respective numbers
to enter the factors. Right click to decrese entered
values.