23. What is the largest common denominator for the fractions below? (Round the answer to the nearest integer.) 1/2, 2/3, 4/5
Answer: A
30
The largest common denominator for the fractions 1/2, 2/3, and 4/5 is 30. This value is determined by finding the least common multiple of the denominators 2, 3, and 5.
A) 30
This option is correct because 30 is the least common multiple of the denominators 2, 3, and 5. It can be divided evenly by all three numbers, making it the largest common denominator for the given fractions.
B) 2
This option is incorrect since while 2 is a common denominator for the fractions, it is not the largest one. In fact, only the fraction 1/2 can be expressed with a denominator of 2 without altering its value, while the other fractions would need to be adjusted.
C) 3
This option is also incorrect because 3 is a common denominator only for the fraction 2/3. It does not work for the other fractions (1/2 and 4/5), making it insufficient as the largest common denominator.
D) 5
This option is incorrect as well because 5 is only a common denominator for the fraction 4/5. The other fractions cannot be represented with a denominator of 5 without changing their values, which disqualifies it from being the largest common denominator.
Conclusion
The answer 30 is definitively the largest common denominator as it accommodates all three fractions simultaneously. All other options fail to serve as a common denominator for all the given fractions, thus underscoring 30's unique suitability for this problem.