What is the result of dividing 5 & 3/4 by 1/2, reduced to the simplest form?

Rationale

Dividing 5 & 3/4 by 1/2 results in 11 & 1/2.

To divide a mixed number by a fraction, first convert the mixed number into an improper fraction. In this case, 5 & 3/4 converts to 23/4. Dividing by 1/2 is the same as multiplying by its reciprocal, thus 23/4 ÷ 1/2 becomes 23/4 × 2/1, which simplifies to 46/4, or 11 & 1/2 in simplest form.

A (5 & 1/2) YOUR ANSWER

This choice suggests a result that is less than the original mixed number, which does not align with the rules of division. Dividing by a fraction typically yields a larger result, and in this case, 5 & 1/2 is significantly lower than the actual quotient of 11 & 1/2.

B (2 & 3/8) YOUR ANSWER

This choice is incorrect because it implies that the result is significantly less than half of the original mixed number. The division of 5 & 3/4 by 1/2 should yield a result greater than 5, making 2 & 3/8 an impossible outcome for this operation.

C (11 & 1/2) CORRECT

This is the correct answer, representing the proper outcome of the division operation. When 5 & 3/4 is divided by 1/2, the calculation yields 11 & 1/2, confirming the result as an accurate representation of the operation.

D (18) YOUR ANSWER

This choice overestimates the result significantly. The division of a mixed number by a fraction cannot exceed the original mixed number multiplied by the reciprocal of the fraction in such a way to yield 18. This choice does not reflect the nature of dividing by a fraction, which tends to increase the value, but not to this extent.

Conclusion

The division of 5 & 3/4 by 1/2 correctly simplifies to 11 & 1/2, demonstrating the process of converting mixed numbers and applying the reciprocal of the divisor. The incorrect options reflect misunderstandings of the division process, while the correct answer accurately represents the mathematical operation performed.

What is the result of dividing 5 & 3/4 by 1/2, reduced to the simplest form?

Dividing 5 & 3/4 by 1/2 results in 11 & 1/2.

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