19. What is 5 & 3/4 divided by 1/2 when reduced?
Answer: C
5 & 3/4 divided by 1/2 equals 11 & 1/2.
To solve the problem, we convert 5 & 3/4 into an improper fraction, which is 23/4. Dividing this by 1/2 is equivalent to multiplying by the reciprocal, resulting in 23/4 * 2/1 = 46/4, which simplifies to 11 & 1/2.
A) 5 & 1/2
This option is incorrect as 5 & 1/2 equals 11/2 or 22/4, which does not match the result of 5 & 3/4 divided by 1/2.
B) 2 & 3/8
This option is also incorrect because 2 & 3/8 converts to 19/8, which is significantly less than the correct answer of 11 & 1/2.
C) 11 & 1/2
This option is correct as the calculation of 5 & 3/4 divided by 1/2 simplifies to 11 & 1/2, confirming it as the accurate result.
D) 18
This option is incorrect since 18 is far greater than the actual result of the division; it does not reflect the calculation performed.
Conclusion
The correct answer, 11 & 1/2, is the only option that accurately represents the result of the division problem. All other options either miscalculate the fraction or misinterpret the division, leading to results that do not align with the correct mathematical principles.