Question 4

3/4 divided by 2/3 equals 9/8.

To find the result of 3/4 divided by 2/3, you multiply 3/4 by the reciprocal of 2/3, which is 3/2. This calculation yields 9/8.

A) 1/2

This option is incorrect because dividing 3/4 by 2/3 does not yield a fraction that simplifies to 1/2. Instead, the operation leads to a larger fraction, as shown in the correct calculation.

B) 9/8

This is the correct answer. When dividing 3/4 by 2/3, you multiply by the reciprocal (3/2), resulting in (3/4) * (3/2) = 9/8. This fraction is greater than 1, which aligns with the expected outcome of the division.

C) 8/9

This option is incorrect because the division of 3/4 by 2/3 does not simplify to 8/9. Instead, it reflects a misunderstanding of the operation, as the result should be greater than 1.

D) 5/12

This choice is also incorrect. The fraction 5/12 does not represent the outcome of dividing 3/4 by 2/3. The correct calculation leads to a fraction that is larger than both 3/4 and 2/3.

Conclusion

The correct answer, 9/8, is derived from the proper application of the division of fractions, specifically by multiplying by the reciprocal. All other options fail to represent the correct mathematical outcome of this division operation, demonstrating a clear understanding of fraction manipulation is essential.