Rationale
20/24 and 21/24 are equivalent to 5/6 and 7/8, respectively.
To determine equivalence, we can simplify or convert the given \fractions. The \fractions 20/24 and 21/24 can be simplified to 5/6 and 7/8, confirming that they are indeed equivalent.
A) 20/48 and 42/48
The \fraction 20/48 simplifies to 5/12, not 5/6, since both the numerator and denominator can be divided by 4. Similarly, 42/48 simplifies to 7/8, but since one \fraction is incorrect, this pair cannot be equivalent to 5/6 and 7/8.
B) 10/12 and 14/12
10/12 simplifies to 5/6, but 14/12 simplifies to 7/6, which exceeds 1 and does not match 7/8. Therefore, while one \fraction is correct, the other does not correspond with the required equivalence.
C) 20/24 and 21/24
Both \fractions can be simplified: 20/24 simplifies to 5/6 and 21/24 simplifies to 7/8. This pair is equivalent to the original \fractions, making it the correct choice.
D) 10/16 and 14/16
10/16 simplifies to 5/8, which is not equivalent to 5/6, and 14/16 simplifies to 7/8. Since only one of the \fractions matches, this pair cannot be equivalent to the given \fractions.
Conclusion
To find equivalent \fractions, one must check if the simplified forms match the original \fractions. The pair 20/24 and 21/24 effectively simplifies to 5/6 and 7/8, respectively, confirming their equivalence. Other options either simplify incorrectly or contain one \fraction that does not match, disqualifying them as answers.
