Question

one method of comparing two fractions for inequalities is to find their decimal representations. use this method to rearrange the fractions in increasing order from left to right.\\(\frac{12}{17}\\) \\(\frac{18}{34}\\) \\(\frac{16}{21}\\) \\(\frac{20}{26}\\) \\(\frac{38}{51}\\)\
multiple choice\
\\(\bigcirc\\) \\(\frac{20}{26} < \frac{16}{21} < \frac{38}{51} < \frac{12}{17} < \frac{18}{34}\\)\
\\(\bigcirc\\) \\(\frac{12}{17} < \frac{38}{51} < \frac{16}{21} < \frac{18}{34} < \frac{20}{26}\\)\
\\(\bigcirc\\) \\(\frac{18}{34} < \frac{12}{17} < \frac{38}{51} < \frac{16}{21} < \frac{20}{26}\\)\
\\(\bigcirc\\) \\(\frac{38}{51} < \frac{16}{21} < \frac{18}{34} < \frac{12}{17} < \frac{20}{26}\\)

Explanation:

Step1: Convert fractions to decimals

$\frac{12}{17} \approx 0.7059$, $\frac{18}{34} \approx 0.5294$, $\frac{16}{21} \approx 0.7619$, $\frac{20}{26} \approx 0.7692$, $\frac{38}{51} \approx 0.7451$

Step2: Sort decimals ascending

$0.5294 < 0.7059 < 0.7451 < 0.7619 < 0.7692$

Step3: Match to original fractions

Replace decimals with corresponding fractions

Answer:

C. $\frac{18}{34} < \frac{12}{17} < \frac{38}{51} < \frac{16}{21} < \frac{20}{26}$