Algebra Balance Scales - Negatives

This virtual manipulative allows you to solve simple linear equations through the use of a balance beam. Unit blocks (representing 1s) and X-boxes (for the unknown, X), are placed on the pans of a balance beam. Once the beam balances to represent the given linear equation, you can choose to perform any arithmetic operation with whole numbers and multiples of the variable 'x', as long as you DO THE SAME THING TO BOTH SIDES, thus keeping the beam balanced. The goal, of course, is to get a single X-box on one side, with however many unit blocks needed for balance, thus giving the value of X.

Placing Blocks and Boxes on the Balance Beam

Click on an object and drag it toward the side of the beam you wish to place it on. When you release the object, it will snap into place on the beam. When you first place an object on a pan, the beam swings down on that side (no longer balances), but when the given equation is fully represented, balance is restored. Note that you cannot click the button until you have represented the equation, whether or not the beam balances. Blocks and boxes may be placed on either pan and in any order. Negative numbers and negative multiples of 'x' have their own bins and act in the opposite way from positives: where a positive number weighs down a pan of the balance beam, a negative number lifts the pan up. Negatives are represented by balloons that lift the pans.

Removing Blocks or Boxes

Click and drag any object (even from the middle of a stack) to the Trash Can in the lower right corner of the workspace.

Solving the Equation

When you have correctly represented the equation, you can click the button. The initial display then shows the ADD option, but you may click on any of the other buttons, to SUBTRACT, MULTIPLY, or DIVIDE. The only allowable operations require that you DO THE SAME THING TO BOTH SIDES of the beam (and thus to both sides of the equation).

Type in what you want to add to or subtract from both sides, and click the button. You can, for example, subtract 2X from both sides, if there are two X-boxes on both sides. You can multiply or divide only by numbers, and only if the operation can be done in whole numbers. Thus if you have an even number of blocks and of X-boxes on both pans of the balance beam, then you can divide both sides by 2, and you might wish to add things to both sides to allow such a division.

The equation is updated with each operation. When you have a single X-box on one pan and blocks on the other pan, the equation displays the solution.