Final Answer:
The new number, obtained by dividing the original number by 2/3, is 1.5 times the original number. Thus, the correct answer is C) The new number is 1.5 times the original number.
Explanation:
When a number is divided by 2/3, it is essentially multiplied by its reciprocal, which is 3/2. Dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore, dividing a number by 2/3 is the same as multiplying it by 3/2.
Let's represent the original number as x. Dividing x by 2/3 can be written as x ÷ {2}\{3} or x × {3}\{2}, which means the new number is x × {3}\{2} or 1.5x.
Hence, the new number, obtained by dividing the original number by 2/3, is 1.5 times the original number, corresponding to option C. This interpretation demonstrates that dividing by 2/3 increases the original number by a factor of 1.5, making the new number 1.5 times larger than the original.
Thus, the correct answer is C) The new number is 1.5 times the original number.