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Visualizing Addition and Subtraction of Fractions
Quick instructions
Each of the four white rectangles in the panel of this applet
represents one unit. A selection of a number from the upper choice box divides the upper
wide rectangle into that number of equal parts. Clicking on the upper "DIV" button
changes its label to "FRA" and allows you to select a certain number of the
consecutive equal parts. This selection is done by clicking on one of the parts
there. Then all preceding parts and the part clicked upon are colored (cyan).
These colored parts constitute a certain fraction of the whole unit. Simultaneously
this fraction is formally recorded on the small blackboard. If the selected fraction
can be simplified (reduced), the simplified notation of it is also displayed.
The same way another fraction in the lower vide
rectangle can be constructed. Its color will be light green.
If you want to change the selected fractions just click on
another part of the selected rectangle. To change the current partition click on the proper
"FRA" button and make a new selection. If you are satisfied with your selection of
fractions click on the "SET" button. This sets the selected fractions and enables
the choice of the least common denominator for the selected fractions.
Making the correct choice divides the parts in both rectangles into the
correct partitions. Only if these conditions are fulfilled will the operation button "+/-"
be activated.
During the selection of the least common denominator the selected partition is
shown in both narrow rectangles. This allows you to see how this partition fits
to the partitions previously selected for the wide rectangles.
When the "+/-" button is activated, select if you want to add
or subtract the fractions. The first click selects addition and you
can toggle between the subtraction and addition as long as none of the wide rectangles
is clicked. This selects the operation (addition or subtraction) and creates
the original fractions in the narrow rectangles with their formal descriptions on
the two additional small blackboards. It also partitions the original fractions in
the wide rectangles in accordance with the selected common denominator.
Holding the mouse button down on one of the colored parts
of any wide rectangle may cause temporary disappearance of this and all colored parts. Now these parts are ready to be moved to the other rectangle. If addition
is selected, the mouse cursor should be dragged to the first white partition in
the other rectangle and the mouse button released there. Then the parts that
disappeared in the first rectangle will show in the other rectangle. When one of
the rectangles is totally filled, the addition process is finalized and you can
analyze its graphic results. The formal results are shown on the two adjacent
blackboards.
In the case of subtraction, the mouse cursor should be
released
over the colored part of the other wide rectangle. Try to remove the same number of colored parts from there as you
have already removed from the first
rectangle. If everything is done correctly they will disappear. Thus the
subtraction process of the colored parts of the lower rectangle from the colored
parts of the upper rectangle will be partially executed. Now you can repeat this
process again. As soon as one of the rectangles does not have any colored parts,
the subtraction process is complete. If some colored parts are left only in the
upper rectangle, the final result is positive. Otherwise it is negative or zero
(if no colored parts are left). The formal results of the performed
operations are shown again on two adjacent small blackboards.
To start a new problem of fraction addition or subtraction
use the "RESET" button at any time.
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