Math Problem 2: One Dollar is 10,000 Cents
It is well-known that 1 dollar = 100 cents. Furthermore, x dollars = 100x cents. Multiplying these two equations together yields 1x dollars = 100 * 100x cents = 10,000x cents, which means that 1 dollar = 10,000 cents.
Where is the logical fallacy?
Consider the problem in different terms. For example, use meters and centimeters instead of dollars and cents (the math is the same).
When multiplying, the units must also be multiplied. Thus, the intermediate equation would be 1x square dollars = 100 * 100x square cents. This problem is often not caught because there is no sense to the unit of "square dollars", but becomes more obvious when using a unit of length such as meters.