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Zorluk: OrtaFraction Operations

A portable generator's fuel tank holds 8148\frac{1}{4} gallons of diesel. If the generator consumes fuel at a rate of 1231\frac{2}{3} gallons per hour, how many gallons of fuel remain in the tank after exactly 22 hours of continuous operation?

  1. 411124\frac{11}{12}Cevap
  2. B
    131613\frac{1}{6}
  3. C
    51125\frac{1}{12}
  4. D
    111121\frac{11}{12}

Cevap

The correct answer is 411124\frac{11}{12} gallons.
The correct answer accurately calculates the total fuel used by multiplying the hourly consumption rate by the operating time (123×2=3131\frac{2}{3} \times 2 = 3\frac{1}{3}). It then correctly subtracts this total from the initial tank capacity by finding a common denominator and borrowing appropriately (814−313=8312−3412=71512−3412=411128\frac{1}{4} - 3\frac{1}{3} = 8\frac{3}{12} - 3\frac{4}{12} = 7\frac{15}{12} - 3\frac{4}{12} = 4\frac{11}{12}).

Adım Adım Çözüm

1
Calculate the total amount of fuel consumed in 2 hours.
2×123=2×53=103=3132 \times 1\frac{2}{3} = 2 \times \frac{5}{3} = \frac{10}{3} = 3\frac{1}{3} gallons
Total consumption is the hourly rate multiplied by the number of hours operated.
2
Set up the subtraction to find the remaining fuel.
814−3138\frac{1}{4} - 3\frac{1}{3}
Remaining fuel is the initial capacity minus the total consumed fuel.
3
Find a common denominator to subtract the mixed numbers.
The least common multiple of 44 and 33 is 1212. The expression becomes 8312−34128\frac{3}{12} - 3\frac{4}{12}.
Fractions must have the same denominator before they can be added or subtracted.
4
Borrow from the whole number to subtract the fractions.
83128\frac{3}{12} becomes 715127\frac{15}{12}. Then, 71512−3412=411127\frac{15}{12} - 3\frac{4}{12} = 4\frac{11}{12} gallons.
Since 312\frac{3}{12} is less than 412\frac{4}{12}, one whole unit must be converted into twelfths (1212\frac{12}{12}) and added to the fraction.

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