A Navy maintenance crew is applying a new non-slip coating to a ship's deck. A single stan… — Armed Services Vocational Aptitude Battery (ASVAB)

A Navy maintenance crew is applying a new non-slip coating to a ship's deck. A single standard drum of the coating covers exactly $12 \frac{3}{4}$ square yards of deck surface. If the crew needs to coat a helicopter landing pad that requires exactly $5 \frac{1}{3}$ times the amount of coating contained in a single drum, what is the total area of the helicopter landing pad in square yards?

Answer: 68 square yards

Answer

To find the total area, you must multiply the area covered by one drum (

12 \frac{3}{4}

square yards) by the relative size of the landing pad (

5 \frac{1}{3}

). Converting to improper fractions gives

\frac{51}{4} \times \frac{16}{3}

. Cross-canceling the terms yields

17 \times 4 = 68

square yards.

Step-by-Step Solution

Convert the mixed numbers

12 \frac{3}{4}

and

5 \frac{1}{3}

to improper fractions.

12 \frac{3}{4} = \frac{12 \times 4 + 3}{4} = \frac{51}{4}

and

5 \frac{1}{3} = \frac{5 \times 3 + 1}{3} = \frac{16}{3}

Multiplication of mixed numbers requires converting them to improper fractions first.

Multiply the two improper fractions to find the total area.

\frac{51}{4} \times \frac{16}{3}

The total area is the area covered by one drum multiplied by the number of drum-equivalents required.

Simplify and compute the final product.

\frac{51 \times 16}{4 \times 3} = \left(\frac{51}{3}\right) \times \left(\frac{16}{4}\right) = 17 \times 4 = 68

Simplifying the fractions by cross-canceling before multiplying makes the calculation easier and provides the final area.

Key Concept

Multiplying mixed numbers by converting them to improper fractions in an applied context.

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