A quartermaster unit has a bulk roll of heavy-duty canvas measuring 71 \frac{1}{4} yards i… — Armed Services Vocational Aptitude Battery (ASVAB)

A quartermaster unit has a bulk roll of heavy-duty canvas measuring $71 \frac{1}{4}$ yards in length. The unit needs to manufacture custom protective covers for equipment, with each cover requiring exactly $3 \frac{3}{4}$ yards of canvas. How many complete protective covers can the unit manufacture from this roll?

Answer: 19 covers

Answer

To find how many items of a specific size can be made from a total amount, you divide the total amount by the size of one item. After converting the mixed numbers to improper fractions (

71 \frac{1}{4} = \frac{285}{4}

and

3 \frac{3}{4} = \frac{15}{4}

), you multiply

\frac{285}{4}

by the reciprocal

\frac{4}{15}

. The denominators and numerators simplify to yield exactly 19.

Step-by-Step Solution

Determine the required mathematical operation.

Division: Total canvas length ÷ Length per cover.

You are distributing a total quantity into equal-sized portions.

Convert the mixed numbers into improper fractions.

71 \frac{1}{4} = \frac{285}{4}

and

3 \frac{3}{4} = \frac{15}{4}

Fraction multiplication and division require working with proper or improper fractions rather than mixed numbers.

Multiply the first fraction by the reciprocal of the second fraction.

\frac{285}{4} \times \frac{4}{15}

Dividing by a fraction is mathematically equivalent to multiplying by its reciprocal.

Simplify the expression and calculate the final quotient.

The 4s cancel, leaving

\frac{285}{15} = 19

Cross-simplifying makes the calculation much more manageable without needing a calculator.

Key Concept

Dividing mixed numbers in applied word problems

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