A carpenter is sorting four wooden planks based on their lengths to construct a custom fra… — Armed Services Vocational Aptitude Battery (ASVAB)

A carpenter is sorting four wooden planks based on their lengths to construct a custom frame. The lengths of the planks, in feet, are listed below. Sequence the plank lengths from shortest to longest.

1 $1\frac{1}{3}$ feet
2 $1\frac{3}{8}$ feet
3 $\frac{7}{5}$ feet
4 $\frac{17}{12}$ feet

Answer

The correct ascending sequence is

1\frac{1}{3}

feet,

1\frac{3}{8}

feet,

\frac{7}{5}

feet, and

\frac{17}{12}

feet.

To compare fractions with different denominators, they must be converted to a common denominator. The least common multiple of

3

8

5

, and

12

120

. Converting all values yields

\frac{160}{120}

\frac{165}{120}

\frac{168}{120}

, and

\frac{170}{120}

. Arranging these from smallest to largest gives the proper sequence of

1\frac{1}{3}

feet,

1\frac{3}{8}

feet,

\frac{7}{5}

feet, and

\frac{17}{12}

feet.

Step-by-Step Solution

Convert all mixed numbers to improper fractions.

1\frac{3}{8} = \frac{11}{8}

and

1\frac{1}{3} = \frac{4}{3}

Fractions must be in a consistent improper format to find a common denominator efficiently.

Find the least common multiple (LCM) for the denominators

8

12

3

, and

5

The LCM of

8

12

3

, and

5

120

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

Convert each fraction to an equivalent fraction with a denominator of

120

\frac{4}{3} = \frac{160}{120}

\frac{11}{8} = \frac{165}{120}

\frac{7}{5} = \frac{168}{120}

, and

\frac{17}{12} = \frac{170}{120}

Normalizing the denominators isolates the variation to the numerators, making comparison straightforward.

Arrange the fractions by comparing their normalized numerators from smallest to largest.

160 < 165 < 168 < 170

, which corresponds to the original values

1\frac{1}{3} < 1\frac{3}{8} < \frac{7}{5} < \frac{17}{12}

The problem specifies sequencing the plank lengths from shortest to longest.

Key Concept

Ordering and Comparing Fractions

Alternative Method

Convert each fraction to its decimal equivalent:

1\frac{1}{3} \approx 1.333

1\frac{3}{8} = 1.375

\frac{7}{5} = 1.400

, and

\frac{17}{12} \approx 1.417

. The decimals can then be easily ordered from least to greatest.

Estimated Time:1m 0s

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Answer

Step-by-Step Solution

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Alternative Method

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