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Zorluk: OrtaFraction Operations

A plumber is connecting three sections of PVC pipe to bridge a gap that is 121412\frac{1}{4} feet wide. The first section of pipe measures 4234\frac{2}{3} feet in length, and the second section measures 3343\frac{3}{4} feet. Assuming there is no overlap between the connected sections, what must be the length of the third section of pipe to exactly bridge the gap?

  1. 3563\frac{5}{6} feetCevap
  2. B
    4164\frac{1}{6} feet
  3. C
    4564\frac{5}{6} feet
  4. D
    202320\frac{2}{3} feet

Cevap

The third section of pipe must be 3563\frac{5}{6} feet long.
The correct answer accurately adds the two pipe lengths by finding a common denominator of 12, resulting in 85128\frac{5}{12}. It then subtracts this sum from the total gap width of 1231212\frac{3}{12} by properly borrowing from the whole number to get 111512−8512=3101211\frac{15}{12} - 8\frac{5}{12} = 3\frac{10}{12}, which simplifies to 3563\frac{5}{6}.

Adım Adım Çözüm

1
Find the combined length of the first two pipe sections.
423+3344\frac{2}{3} + 3\frac{3}{4}
To determine how much of the gap has already been covered.
2
Convert the fractions to a common denominator and add.
4812+3912=717124\frac{8}{12} + 3\frac{9}{12} = 7\frac{17}{12}
The least common multiple of 3 and 4 is 12.
3
Simplify the improper fraction.
71712=7+1512=85127\frac{17}{12} = 7 + 1\frac{5}{12} = 8\frac{5}{12} feet
Converting to a proper mixed number makes the final subtraction step accurate.
4
Subtract the combined length from the total gap width.
1214−8512=12312−851212\frac{1}{4} - 8\frac{5}{12} = 12\frac{3}{12} - 8\frac{5}{12}
The remaining distance requires subtracting the covered distance from the total.
5
Borrow from the whole number to perform the subtraction.
111512−8512=31012=35611\frac{15}{12} - 8\frac{5}{12} = 3\frac{10}{12} = 3\frac{5}{6} feet
Since 312\frac{3}{12} is smaller than 512\frac{5}{12}, you must borrow 1 whole (or 1212\frac{12}{12}) from 12.

Anahtar Kavram

Fraction Operations with Mixed Numbers
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Fraction Operations

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