A logistics specialist is organizing four replacement fuel hoses by length. The lengths ar… — Armed Services Vocational Aptitude Battery (ASVAB)

A logistics specialist is organizing four replacement fuel hoses by length. The lengths are $\frac{17}{4}$ meters, $4 \frac{3}{8}$ meters, $\frac{14}{3}$ meters, and $4 \frac{5}{12}$ meters. Arrange these hose lengths in ascending order from shortest to longest.

1 $\frac{17}{4}$ meters
2 $4 \frac{3}{8}$ meters
3 $4 \frac{5}{12}$ meters
4 $\frac{14}{3}$ meters

Answer

The correct ascending order is

\frac{17}{4}

meters,

4 \frac{3}{8}

meters,

4 \frac{5}{12}

meters, and

\frac{14}{3}

meters.

By converting all values to mixed numbers with a common denominator of 24, the fractional parts become

\frac{6}{24}

\frac{9}{24}

\frac{10}{24}

, and

\frac{16}{24}

. Ordering these from smallest to largest provides the correct sequence.

Step-by-Step Solution

Convert the improper fractions to mixed numbers for easier comparison.

\frac{17}{4} = 4 \frac{1}{4}

and

\frac{14}{3} = 4 \frac{2}{3}

Comparing values is simpler when whole numbers and fractional parts are separated.

Identify the fractional parts to be compared.

Since all lengths share a whole number of 4, we only need to compare the fractions:

\frac{1}{4}

\frac{3}{8}

\frac{5}{12}

, and

\frac{2}{3}

The whole numbers are identical, so the overall size depends entirely on the fractional parts.

Find a common denominator for the fractions 4, 8, 12, and 3.

The least common multiple (LCM) of the denominators 4, 8, 12, and 3 is 24.

A common denominator is required to directly and accurately compare the sizes of the numerators.

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

\frac{1}{4} = \frac{6}{24}

;

\frac{3}{8} = \frac{9}{24}

;

\frac{5}{12} = \frac{10}{24}

;

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

This standardizes the fractions so their relative sizes are visually clear.

Order the fractions from smallest to largest based on their numerators.

\frac{6}{24} < \frac{9}{24} < \frac{10}{24} < \frac{16}{24}

, which corresponds to

\frac{17}{4} < 4 \frac{3}{8} < 4 \frac{5}{12} < \frac{14}{3}

Ordering the standardized fractions reveals the correct ascending sequence for the original lengths.

Key Concept

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

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Step-by-Step Solution

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