DragginMath: Rules of Signs

Enter – – – – -a. This picture looks different from the others we have seen. This is less of a tree and more of a stalk, because it is composed of only unary operators. Drag a onto the topmost operator. The result is -a. This is because two negations are the same as nothing at all. In this example, two separate pairs of negate operators cancelled each other out, and only one negate remains.

Enter ÷ ÷ ÷ ÷ ÷a. This becomes ⅟⅟⅟⅟⅟a. Drag a onto the topmost operator. The result is ⅟a. This is because two reciprocals are the same as nothing at all. In this example, two separate pairs of reciprocate operators cancelled each other out, and only one reciprocate remains.

Enter – ⅟-⅟⅟- – ⅟a. Drag a onto the topmost operator. The result is a. In this example, all of these sign operators cancelled each other out. They don’t need to be grouped together by kind in order to do that.

Whenever you ask DragginMath to do anything in an operator tree, it first simplifies the sign operators in that part of the tree. Then it does the thing you wanted.

Enter – ⅟a. Drag ⅟ up onto –. The result is ⅟-a. Now drag – up onto ⅟. The result is – ⅟a.

Enter -(ab). Drag a onto –. The result is -a∗b.

Enter -(ab) again. Drag b onto –. The result is a∗-b.

DragginMath can move sign operators into various places you might want them to be. This is critical to some solutions. DragginMath won’t move sign operators into places it knows they don’t belong.

Negate – and reciprocate ⅟ are not the only sign operators DragginMath knows about. Another is the unary form of plus-and-minus ±. This coalesces with itself and with negate, so ± – ±a reduces simply to ±a. Is this useful? Yes. If you ever transformed ax↑2+bx+c=0 into x=(-b±√(b↑2-4ac))÷(2a) on paper, you might not have noticed this little thing when you did it.