Pan Balance

(use with UCSMP Transition Mathematics, Lessons 5-5, 8-6, 8-8, 9-5, 10-2)

If you can't see the demo above, click here.


This applet is designed to help you learn different techniques to solve linear equations. To create a new equation simply type in the coefficients and constants in the boxes at the bottom left of the balance. Then hit the ENTER button. Or you can hit the RANDOM EQUATION button to solve a new equation. There are two main ways to simplify your equation using this program. You can add values to each side and you can multiply or divide each side by a number.

To Add to both sides

On the rightmost part of the screen you will see several blocks. You can add any of these to the scale simply by dropping it above either one of the pans. However if you only add to one side, this will unbalance the scale and your equation! To fix this simply drag the same block over to the other side of the scale. This will rebalance the scale (and the equations) and if you chose you weights carefully the equation will now be simpler.

To Multiply or Divide each side

On the bottom of the screen you will see a label displaying DIVIDE/MULTIPLY. In the text area enter the number you wish to multiply or divide each side by and then click the appropriate operation button. Each side will then be multiplied (or divided) by the given amount.

Additional Notes

  • You may want to add a weight to both sides that is not already present on the right side of the balance. To do this, simply type a value into the "Add New Weight" box, and then hit the NEW WEIGHT button.
  • All the boxes at the bottom of the balance are able to accept numbers in decimal or fractional form
  • After performing several operations you should hit the SIMPLIFY button in the bottom right corner to consolidate the weights.
  • If you make a mistake or end up with an equation you can't rebalance simply use the UNDO button in the bottom right corner to go back several steps.