Which set of fractions is ordered from least to greatest

Which set of fractions is ordered from least to greatest? A) 5/8, 8/12, 3/4 B) 8/12, 5/8, 3/4 C) 3/4, 5/8, 8/12 D) 5/8, 3/4, 8/12

The Correct Answer and Explanation is:

The correct answer is A) 5/8, 8/12, 3/4.

Explanation:

To order fractions from least to greatest, we need to compare their values. A common method is to convert each fraction to a decimal or find a common denominator.

1. Convert each fraction to a decimal:
   • 58=0.625\frac{5}{8} = 0.62585​=0.625
   • 812=23=0.6667\frac{8}{12} = \frac{2}{3} = 0.6667128​=32​=0.6667 (rounded)
   • 34=0.75\frac{3}{4} = 0.7543​=0.75
   In decimal form, the fractions are:
   • 0.6250.6250.625 (for 58\frac{5}{8}85​)
   • 0.66670.66670.6667 (for 812\frac{8}{12}128​)
   • 0.750.750.75 (for 34\frac{3}{4}43​)
   So, the order from least to greatest is:
   • 58<812<34\frac{5}{8} < \frac{8}{12} < \frac{3}{4}85​<128​<43​.
2. Verify using a common denominator:
   The least common denominator (LCD) of 8, 12, and 4 is 24. We can rewrite each fraction with a denominator of 24:
   • 58=1524\frac{5}{8} = \frac{15}{24}85​=2415​
   • 812=1624\frac{8}{12} = \frac{16}{24}128​=2416​
   • 34=1824\frac{3}{4} = \frac{18}{24}43​=2418​
   Again, the order is:
   • 1524<1624<1824\frac{15}{24} < \frac{16}{24} < \frac{18}{24}2415​<2416​<2418​, which corresponds to 58<812<34\frac{5}{8} < \frac{8}{12} < \frac{3}{4}85​<128​<43​.

Thus, the correct answer is A) 5/8, 8/12, 3/4.