What is 5 & 3/4 divided by 1/2 when reduced?

Rationale

5 & 3/4 divided by 1/2 equals 11 & 1/2.

To divide a fraction by another fraction, you multiply by the reciprocal of the divisor. In this case, dividing 5 & 3/4 (which is the same as 23/4) by 1/2 is equivalent to multiplying 23/4 by 2/1, resulting in 46/4 or 11 & 1/2 when reduced.

A (5 & 1/2) YOUR ANSWER

This choice suggests a total that is significantly lower than the correct calculation. Dividing 5 & 3/4 (23/4) by 1/2 would not yield 5 & 1/2, which is equivalent to 11/2 or 5.5. The result of the division is clearly greater than this value.

B (2 & 3/8) YOUR ANSWER

This result would imply that the division has produced a much smaller quotient than anticipated. Specifically, 2 & 3/8 equals 19/8, which is far less than the expected output of 5 & 3/4 divided by 1/2. The actual division yields a number that is close to 11, not 2.375.

C (11 & 1/2) CORRECT

This option correctly represents the result of dividing 5 & 3/4 by 1/2. Converting 5 & 3/4 to an improper fraction (23/4) and multiplying it by the reciprocal of 1/2 (which is 2) results in 46/4, which simplifies to 11 & 1/2.

D (18) YOUR ANSWER

This choice is far too high and suggests a miscalculation. The quotient of dividing 5 & 3/4 by 1/2 cannot exceed 12, as indicated by the calculation. The correct answer of 11 & 1/2 is a clear indication that 18 is not a plausible outcome.

Conclusion

When dividing mixed numbers, it’s essential to convert them into improper fractions and then multiply by the reciprocal of the divisor. In this case, the division of 5 & 3/4 by 1/2 correctly simplifies to 11 & 1/2, making it the only valid answer among the choices provided. Each of the incorrect options either underestimates or overestimates the result of the division.

What is 5 & 3/4 divided by 1/2 when reduced?

5 & 3/4 divided by 1/2 equals 11 & 1/2.

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