Which of the following inequalities is correct?
3/5 < 2/3 < 5/7.
To determine the correct order of the fractions, we can convert them to a common denominator or convert them to decimal form. Comparing these values shows that 3/5 is less than 2/3, which is in turn less than 5/7.
This inequality suggests that 2/3 is less than 3/5. However, when we convert to decimal, 2/3 equals approximately 0.6667, and 3/5 equals 0.6, indicating that 2/3 is greater than 3/5, thus making this statement incorrect.
This statement incorrectly positions 2/3 as less than both 5/7 and 3/5. In decimal form, 5/7 is approximately 0.7143, which is greater than 2/3. Consequently, this ordering does not hold true, making it an incorrect choice.
This inequality is correct as established through comparison. 3/5 is 0.6, which is less than 2/3 (approximately 0.6667), and 2/3 is less than 5/7 (approximately 0.7143). Therefore, this statement accurately reflects the correct relationships among the fractions.
This option misplaces 2/3 as the largest value. Although 3/5 is indeed less than 5/7, the comparison fails when it comes to 2/3, which is actually less than 5/7. Therefore, this choice is incorrect.
The correct inequality order is established as 3/5 < 2/3 < 5/7. By comparing decimal values, we verified the relationships among the fractions, highlighting that 3/5 is the smallest and 5/7 is the largest. Each incorrect choice misrepresents the relationships among these fractions, emphasizing the importance of understanding and accurately comparing fractional values.
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