An aviation structural mechanic is cutting a piece of sheet metal to repair an aircraft fu… — Armed Services Vocational Aptitude Battery (ASVAB)

An aviation structural mechanic is cutting a piece of sheet metal to repair an aircraft fuselage. The initial piece of sheet metal is $45 \frac{1}{2}$ inches long. The mechanic cuts off one piece that is $14 \frac{3}{4}$ inches long and another piece that is $18 \frac{5}{8}$ inches long. Assuming no material is lost to the saw cut, how many inches of the sheet metal remain? (Enter your answer as a decimal).

Cevap: 12.125 inches

Cevap

The remaining piece of sheet metal is 12.125 inches long.

The remaining length is correctly found by determining the sum of the removed parts (

14 \frac{3}{4} + 18 \frac{5}{8} = 33 \frac{3}{8}

) and subtracting it from the whole (

45 \frac{1}{2} - 33 \frac{3}{8} = 12 \frac{1}{8}

), which equals 12.125 inches.

Adım Adım Çözüm

Find a common denominator for the fractional parts to easily add and subtract the lengths.

The least common denominator for 2, 4, and 8 is 8. The initial length is

45 \frac{4}{8}

inches. The first cut is

14 \frac{6}{8}

inches, and the second cut is

18 \frac{5}{8}

inches.

Fractions must have the same denominator before they can be added or subtracted.

Calculate the total length of the sheet metal that was cut off.

14 \frac{6}{8} + 18 \frac{5}{8} = 32 \frac{11}{8}

, which simplifies to

33 \frac{3}{8}

inches.

Adding the cut pieces together gives the total amount of material removed.

Subtract the total cut length from the initial length to find the remaining amount.

45 \frac{4}{8} - 33 \frac{3}{8} = 12 \frac{1}{8}

inches.

Subtracting the removed material from the starting material leaves the remaining balance.

Convert the final mixed number to a decimal.

12 \frac{1}{8} = 12.125

The question requires a decimal format for the numeric entry.

Anahtar Kavram

Adding and subtracting mixed numbers with unlike denominators in a practical context.

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