Arrange the following fractions and mixed numbers in ascending order (from least to greate… — Armed Services Vocational Aptitude Battery (ASVAB)

Arrange the following fractions and mixed numbers in ascending order (from least to greatest).

The correct ascending order is

\frac{14}{9}

1\frac{5}{8}

1\frac{2}{3}

, and

\frac{7}{4}

By converting all values to improper fractions and finding a common denominator of 72, the values become

\frac{112}{72}

\frac{117}{72}

\frac{120}{72}

, and

\frac{126}{72}

. Comparing the numerators allows us to determine the correct ascending order of the original values.

Convert all mixed numbers to improper fractions.

1\frac{5}{8} = \frac{13}{8}

and

1\frac{2}{3} = \frac{5}{3}

Improper fractions are easier to evaluate when finding a common denominator.

Determine the least common multiple (LCM) of the denominators 9, 8, 3, and 4.

The LCM is 72.

A common denominator is required to accurately compare the sizes of fractions.

Convert each fraction into an equivalent fraction with a denominator of 72.

\frac{14}{9} = \frac{112}{72}

\frac{13}{8} = \frac{117}{72}

\frac{5}{3} = \frac{120}{72}

\frac{7}{4} = \frac{126}{72}

Having a common denominator allows for direct comparison of the numerators.

Compare the numerators to order the fractions from least to greatest.

112 < 117 < 120 < 126

, which means

\frac{112}{72} < \frac{117}{72} < \frac{120}{72} < \frac{126}{72}

The question specifies arranging the values in ascending order.

Map the ordered fractions back to their original forms.

\frac{14}{9}

1\frac{5}{8}

1\frac{2}{3}

\frac{7}{4}

To provide the final answer using the exact values given in the prompt.

Comparing and ordering mixed numbers and improper fractions with unlike denominators by finding a common denominator.

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