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jmc

prealgebra junior

Problem

What is the correct ordering of the three numbers

\frac{5}{19}

,

\frac{7}{21}

, and

\frac{9}{23}

, in increasing order?

(A)

\frac{9}{23} < \frac{7}{21} < \frac{5}{19}

(B)

\frac{5}{19} < \frac{7}{21} < \frac{9}{23}

(C)

\frac{9}{23} < \frac{5}{19} < \frac{7}{21}

(D)

\frac{5}{19} < \frac{9}{23} < \frac{7}{21}

Solution

The value of

\frac{7}{21}

is

\frac{1}{3}

. Now we give all the fractions a common denominator.

\frac{5}{19} ⟹ \frac{345}{1311}

\frac{1}{3} ⟹ \frac{437}{1311}

\frac{9}{23} ⟹ \frac{513}{1311}

Ordering the fractions from least to greatest, we find that they are in the order listed. Therefore, our final answer is

\frac{5}{19} < \frac{7}{21} < \frac{9}{23}

.

Final answer

B