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

2 \frac{7}{12}

2 \frac{5}{8}

\frac{8}{3}

, and

\frac{11}{4}

By converting all values to mixed numbers with a common denominator of 24, we find their fractional parts are

\frac{14}{24}

\frac{15}{24}

\frac{16}{24}

, and

\frac{18}{24}

. Because all whole numbers are 2, the order of the original fractions matches the ascending order of these fractional parts.

Convert the improper fractions to mixed numbers to simplify comparison.

\frac{11}{4} = 2 \frac{3}{4}

and

\frac{8}{3} = 2 \frac{2}{3}

. The other numbers are already mixed numbers:

2 \frac{5}{8}

and

2 \frac{7}{12}

Because all the whole numbers are 2, we only need to compare their fractional parts to determine the order.

Identify the least common denominator (LCD) for the fractional parts:

\frac{3}{4}

\frac{5}{8}

\frac{7}{12}

, and

\frac{2}{3}

The denominators are 4, 8, 12, and 3. The lowest number they all divide into evenly is 24.

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

Convert each fractional part to an equivalent fraction with a denominator of 24.

\frac{3}{4} = \frac{18}{24}

\frac{5}{8} = \frac{15}{24}

\frac{7}{12} = \frac{14}{24}

, and

\frac{2}{3} = \frac{16}{24}

Multiplying both the numerator and denominator by the same value preserves the fraction's overall mathematical value.

Order the converted fractions from least to greatest based on their numerators.

\frac{14}{24} < \frac{15}{24} < \frac{16}{24} < \frac{18}{24}

When denominators are equal, a larger numerator represents a larger overall value.

Match the ordered fractions back to their original given forms.

2 \frac{7}{12}

(from

\frac{14}{24}

2 \frac{5}{8}

(from

\frac{15}{24}

\frac{8}{3}

(from

\frac{16}{24}

), and

\frac{11}{4}

(from

\frac{18}{24}

The final answer must present the exact numbers provided in the original stem.

Comparing and Ordering Fractions with Unlike Denominators

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