DragginMath: Double-Tap to Evaluate

Tap the Top Text and enter 8÷2+3. Double-tap ÷ to see the result 4+3. Double-tap + to see the result 7. Undo twice ↩️↩️ to see 8÷2+3 again. Double-tap + again to see the result 7. What just happened?

When you double-tap an operator node, DragginMath evaluates its subtree. You can evaluate the individual operators in a complicated tree, or do them all at once. Use this tool to see as much detail as you need to help you understand what you are doing. Or if you don’t need to see all the details, double-tap the root of the tree to see the final result.

DragginMath only does integer arithmetic. This is intentional. If you need to see decimal fractions, use your calculator.

If you evaluate 12÷4, the result is 3. But if you evaluate 4÷12, the result is 1÷3, which is the equivalent fraction in lowest terms. Because it only does integer arithmetic, 1÷3 is as far as DragginMath will go. And in the context of an algebra class, this is the correct result.

Evaluate or Expand?

Evaluation only gives a numeric result if all of the operands are numbers. If there are any variables in the subtree, DragginMath will still try to evaluate it. But if any evaluation happens at all, it will be an expansion. For example, enter (2+3)↑2, then double-tap ↑ to see the result 25. Now enter (a+b)↑2, then double-tap ↑ to see the result aa+(ab+ba)+bb. Notice that the two expressions (2+3)↑2 and (a+b)↑2 have the same algebraic shape, and DragginMath tries to do the same thing with both of them. But it can’t finish the evaluation of (a+b)↑2 because it doesn’t know the values of a and b. Instead, it does what it can with them and leaves the expanded but unevaluated results in place. This is one of DragginMath’s most powerful features.

Evaluate vs. Cancel

Evaluation is simple and powerful, but it isn’t always the right choice of actions. For example, if you evaluate 3−3, you get 0, but if you evaluate a−a, you still get a−a when you probably wanted 0. If you evaluate 3÷3, you get 1, but if you evaluate a÷a, you still get a÷a when you probably wanted 1. In all of these cases, it is better to cancel (drag toward).

Evaluate Plus-and-Minus (Wobble) ±

Plus-and-Minus ± looks like an operator, but it isn’t one. It is really more of a troublesome notational convenience. In some ways, it is not very convenient at all. Expressions containing ± actually imply the existence of two expressions: one with + and the other with −. Attempting to evaluate an expression like this by double-tapping its root will only go as far as ±. To proceed, you must deliberately double-tap the ±. The single expression will be replaced on the screen and in the Top Text with two expressions: one with + and the other with −. Then you can move forward with each of these separately.

The name Wobble is perhaps a little goofy, but it is also reasonably descriptive, and also easier to say than Plus-or-Minus. Feel free to use it if you are so inclined, but don’t be surprised if people look at you funny when you do.