A carpenter is sorting four wooden dowels of different diameters. Order the dowel diameter… — Armed Services Vocational Aptitude Battery (ASVAB)

A carpenter is sorting four wooden dowels of different diameters. Order the dowel diameters from thinnest to thickest.

The correct order from thinnest to thickest is

\frac{5}{8}

inch,

\frac{3}{4}

inch,

1 \frac{1}{4}

inches, and

\frac{3}{2}

inches.

By converting all fractions and mixed numbers to have a common denominator of

8

, we get

\frac{6}{8}

\frac{5}{8}

\frac{12}{8}

, and

\frac{10}{8}

. Ordering these by numerator from least to greatest gives

\frac{5}{8}

\frac{6}{8}

\frac{10}{8}

\frac{12}{8}

, which corresponds to the original values

\frac{5}{8}

\frac{3}{4}

1 \frac{1}{4}

\frac{3}{2}

Identify a common denominator to compare all fractions easily.

The denominators are

4

8

2

, and

4

. The least common multiple for these is

8

Fractions must have the same denominator to compare their sizes accurately.

Convert each measurement to an equivalent fraction with a denominator of

8

\frac{3}{4} = \frac{6}{8}

\frac{5}{8} = \frac{5}{8}

\frac{3}{2} = \frac{12}{8}

, and

1 \frac{1}{4} = \frac{5}{4} = \frac{10}{8}

This allows for direct comparison of the numerators.

Order the converted fractions by comparing their numerators from smallest to largest.

Comparing the numerators (

5 < 6 < 10 < 12

), the order is

\frac{5}{8}

\frac{6}{8}

\frac{10}{8}

\frac{12}{8}

When denominators are equal, the fraction with the smaller numerator represents a smaller value.

Match the ordered fractions back to their original given forms.

The final order is

\frac{5}{8}

inch,

\frac{3}{4}

inch,

1 \frac{1}{4}

inches, and

\frac{3}{2}

inches.

The question asks to order the original measurements.

Comparing and Ordering Fractions

Convert all fractions to decimals to compare them:

\frac{3}{4} = 0.75

\frac{5}{8} = 0.625

\frac{3}{2} = 1.5

, and

1 \frac{1}{4} = 1.25

. Then order the decimals:

0.625, 0.75, 1.25, 1.5

Estimated Time:45s

Question