You are organizing a shop toolbox and must arrange a mixed set of combination wrenches by … — Armed Services Vocational Aptitude Battery (ASVAB)

You are organizing a shop toolbox and must arrange a mixed set of combination wrenches by their exact jaw opening size. To ensure the correct wrench is selected for tight-tolerance applications without rounding fasteners, arrange the following wrench sizes in order from SMALLEST to LARGEST.

11/2 inch wrench
213 mm wrench
314 mm wrench
49/16 inch wrench
515 mm wrench

Answer

The correct order from smallest to largest is: 1/2 inch, 13 mm, 14 mm, 9/16 inch, and 15 mm.

To accurately compare SAE (fractional) and Metric wrench sizes, all measurements must be converted to a single standard decimal value (typically inches). Using the conversion factor of

1 \text{ inch} = 25.4 \text{ mm}

, we can calculate the exact jaw opening sizes:

Wrench Size	System	Decimal Equivalent
1/2 inch	SAE	$0.5000\text{''}$
13 mm	Metric	$\approx 0.5118\text{''}$
14 mm	Metric	$\approx 0.5512\text{''}$
9/16 inch	SAE	$0.5625\text{''}$
15 mm	Metric	$\approx 0.5906\text{''}$

By comparing the decimal values, it is clear that the correct ascending order is

\frac{1}{2}\text{''}

13 \text{ mm}

14 \text{ mm}

\frac{9}{16}\text{''}

, and

15 \text{ mm}

. Using a wrench even a few thousandths of an inch too large can round the corners off a stubborn fastener.

Step-by-Step Solution

Convert all metric wrench sizes to decimal inches by dividing by 25.4 (since

1 \text{ inch} = 25.4 \text{ mm}

13 \text{ mm} \approx 0.5118 \text{ inches}

14 \text{ mm} \approx 0.5512 \text{ inches}

, and

15 \text{ mm} \approx 0.5906 \text{ inches}

Establishing a common unit of measurement (decimal inches) is strictly required to compare SAE and Metric sizes accurately.

Convert fractional SAE sizes to decimal inches by dividing the numerator by the denominator.

\frac{1}{2} \text{ inch} = 0.5000 \text{ inches}

and

\frac{9}{16} \text{ inch} = 0.5625 \text{ inches}

Fractions must be converted to decimals to allow for direct numerical comparison with the converted metric sizes.

Compare all decimal values and arrange them in ascending order.

0.5000 < 0.5118 < 0.5512 < 0.5625 < 0.5906

, which corresponds to

\frac{1}{2}\text{''}

13 \text{ mm}

14 \text{ mm}

\frac{9}{16}\text{''}

, and

15 \text{ mm}

This mathematical comparison prevents tool selection errors that could round off fastener heads.

Key Concept

Wrench Size Conversion (SAE vs. Metric)

Estimated Time:2m 0s

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