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Difficulty: MediumUS Customary Linear Measurements

An awning installer is measuring canvas fabric for two separate storefronts. The first storefront requires a continuous fabric length of 1341 \frac{3}{4} yards. The second storefront requires a length of 2122 \frac{1}{2} yards. What is the total length of canvas required for both storefronts, expressed in feet and inches?

  1. A
    44 feet 33 inches
  2. B
    1010 feet 33 inches
  3. C
    1111 feet 00 inches
  4. 1212 feet 99 inchesAnswer

Answer

1212 feet 99 inches
The correct answer is derived by first successfully adding the two mixed fractions (134+2121 \frac{3}{4} + 2 \frac{1}{2}) to find a total of 4144 \frac{1}{4} yards. Converting this length to feet requires multiplying by 33, yielding 123412 \frac{3}{4} feet. Finally, the remaining 34\frac{3}{4} of a foot is converted to inches by multiplying by 1212, resulting in exactly 1212 feet and 99 inches.

Step-by-Step Solution

1
Add the two yardage amounts together by finding a common denominator.
134+224=354=4141 \frac{3}{4} + 2 \frac{2}{4} = 3 \frac{5}{4} = 4 \frac{1}{4} yards.
To find the total amount of canvas needed, the fractional values must be combined correctly.
2
Convert the total yards into feet by multiplying by 3.
414×3=174×3=514=12344 \frac{1}{4} \times 3 = \frac{17}{4} \times 3 = \frac{51}{4} = 12 \frac{3}{4} feet.
Because there are 3 feet in 1 yard, multiplying the yardage by 3 gives the equivalent measurement in feet.
3
Convert the fractional portion of the foot into inches by multiplying by 12.
34×12=364=9\frac{3}{4} \times 12 = \frac{36}{4} = 9 inches. The final combined measurement is 1212 feet 99 inches.
Standard linear measurements require any fraction of a foot to be expressed in inches (12 inches = 1 foot).

Key Concept

Converting Mixed Customary Linear Units
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Topics

US Customary Linear Measurements

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