DragginMath: Sharing Factors

If you are teaching or learning fractional arithmetic, DragginMath can now help you by Sharing Factors, also known as making common denominators: drag a denominator or denominator factor onto + above the fraction’s ÷ to see that factor multiplying and dividing the other operand of +. For example, in 2÷3+4÷5, drag 3 onto + to see 2÷3+4∗3÷(3∗5). Then drag 5 onto + to see 2∗5÷(3∗5)+4∗3÷(3∗5). Now you can factor the (3∗5) denominators to see (2∗5+4∗3)÷(3∗5). If that seems complicated, fractional arithmetic is complicated, but it is now easy to do just by dragging. If you still aren’t sure about this, turn on Traditional Text and watch it that way.

This also works for − and ±. And if you have a chain of fractions under any combination of the + − ± operators, drag the factor to the top of that operator chain to see the factor distributed amongst all of the operands. For example, in 2÷3+4−5, drag 3 onto − to see 2÷3+4∗3÷3−5∗3÷3.

As usual, DragginMath is sophisticated about what it will and won’t do here, in this case based on what actually is a denominator factor. For example, in 2÷(3↑4÷5)+6, legitimate denominator factors are 3↑4÷5, 3↑4, and 3. Any of these can be distributed by dragging to the +. But 4 is an exponent, and 5 is actually part of the numerator of the simplified fraction, so attempting to distribute them will quietly fail in the usual DragginMath way.

If you double-tap to evaluate these expressions, DragginMath has always implicitly done what is described here. Now you can step through the process explicitly to help you teach or learn it.