100 p e nn y i s n ′ t 10 p e nn y × 10 p e nn y 100 p e nn y = 10 × 10 p e nn y − − − − − − − − − − − − − − − − − − − 10 p e nn y × 10 p e nn y = 100 p e nn y 2 !!!!
Attempting to multiply currency units like 'penny' improperly led to the incorrect conclusion that 1 pound equals 1 penny. The proper conversion between pounds and ounces in weight utilizes a fixed ratio of 16 ounces to 1 pound, in which multiplication or division is used depending on whether you are moving from a larger to a smaller unit or vice versa.
The initial statement presents a common puzzling question that misuses mathematical operations and unit conversion to lead to an incorrect conclusion. The incorrect reasoning suggests that one pound equals one penny through incorrect multiplication of units.
Firstly, the premise that 1 pound equals 100 pennies is correct. However, 'penny' in this context is used as a unit of currency, not weight or another measurable dimension. The statement '10 penny x 10 penny' is not valid as it implies a multiplication of currency, while currency units are not physical quantities that can be multiplied by each other. The correct method to convert pounds to ounces is to use the established equivalence that 1 pound = 16 ounces. To convert pounds to ounces, you multiply the number of pounds by 16. For example:
3 pounds is equivalent to 48 ounces (3 x 16 = 48).
4(1/2) pounds is equivalent to 72 ounces (4(1/2)×16 = 72).
When you wish to convert ounces back to pounds, you would divide the number of ounces by 16, since you're moving from a smaller unit to a larger one. For instance, 32 ounces would be equal to 2 pounds (32 ÷ 16 = 2).
The student's confusion lies in a flawed mathematical manipulation that incorrectly equates 1 pound to 1 penny. In reality, 1 pound is equivalent to 100 pennies, establishing a direct unit relationship. Proper conversions respect this relationship and prevent contradictions in mathematical expressions.
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