An apprentice mechanic is organizing a set of small fractional SAE ignition wrenches on a … — Armed Services Vocational Aptitude Battery (ASVAB)

An apprentice mechanic is organizing a set of small fractional SAE ignition wrenches on a shop organizer rack. Arrange the following wrench opening sizes in order from smallest to largest opening width:

1 $1/4\text{ in}$
2 $9/32\text{ in}$
3 $5/16\text{ in}$
4 $11/32\text{ in}$
5 $3/8\text{ in}$

Answer

The correct order from smallest to largest wrench opening is

1/4\text{ in}

9/32\text{ in}

5/16\text{ in}

11/32\text{ in}

, and

3/8\text{ in}

To arrange fractional SAE wrenches from smallest to largest, express each dimension with a common denominator of

32

1/4\text{ in} = 8/32\text{ in}

9/32\text{ in} = 9/32\text{ in}

5/16\text{ in} = 10/32\text{ in}

11/32\text{ in} = 11/32\text{ in}

, and

3/8\text{ in} = 12/32\text{ in}

. Comparing the numerators confirms that

8 < 9 < 10 < 11 < 12

, establishing the ascending sequence:

1/4\text{ in}

9/32\text{ in}

5/16\text{ in}

11/32\text{ in}

, and

3/8\text{ in}

Step-by-Step Solution

Find the least common denominator for all given fractional wrench sizes (

4

32

16

, and

8

The common denominator is

32

Converting all fractions to a common denominator allows for a direct comparison of their numerators.

Convert each fraction into equivalent thirty-seconds of an inch.

1/4\text{ in} = 8/32\text{ in}

9/32\text{ in} = 9/32\text{ in}

5/16\text{ in} = 10/32\text{ in}

11/32\text{ in} = 11/32\text{ in}

, and

3/8\text{ in} = 12/32\text{ in}

Multiplying both numerator and denominator by the appropriate factor preserves fractional value while standardizing units.

Arrange the values in ascending order by comparing their numerators.

8/32\text{ in} < 9/32\text{ in} < 10/32\text{ in} < 11/32\text{ in} < 12/32\text{ in}

, which corresponds to

1/4\text{ in} < 9/32\text{ in} < 5/16\text{ in} < 11/32\text{ in} < 3/8\text{ in}

Comparing numerators across equal denominators establishes the exact physical progression of tool opening sizes.

Key Concept

Fractional SAE wrench sizing and common denominator conversion

Estimated Time:1m 0s

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