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Difficulty: MediumFraction Operations

An electrician has a spool containing 251625\frac{1}{6} yards of copper wire. They use 7127\frac{1}{2} yards of the wire for a kitchen circuit and 8348\frac{3}{4} yards for a living room circuit. How many yards of wire are left on the spool?

  1. A
    91129\frac{1}{12}
  2. B
    9129\frac{1}{2}
  3. 811128\frac{11}{12}Answer
  4. D
    2651226\frac{5}{12}

Answer

The correct answer is 811128\frac{11}{12} yards.
First, the total wire used must be calculated by adding 7127\frac{1}{2} and 8348\frac{3}{4}. Using a common denominator of 4, 724+834=15547\frac{2}{4} + 8\frac{3}{4} = 15\frac{5}{4}, which simplifies to 161416\frac{1}{4}. Next, subtract this total from the initial amount on the spool: 2516−161425\frac{1}{6} - 16\frac{1}{4}. The common denominator for 6 and 4 is 12, resulting in 25212−1631225\frac{2}{12} - 16\frac{3}{12}. Since 3 cannot be subtracted from 2, you must borrow 1 from 25, turning it into 24141224\frac{14}{12}. Finally, 241412−16312=8111224\frac{14}{12} - 16\frac{3}{12} = 8\frac{11}{12}.

Step-by-Step Solution

1
Determine the total amount of wire used by adding 7127\frac{1}{2} and 8348\frac{3}{4}.
161416\frac{1}{4} yards
The total wire consumed is the sum of the pieces used for the kitchen and the living room.
2
Find a common denominator to subtract the total used wire from the initial amount: 2516−161425\frac{1}{6} - 16\frac{1}{4}.
25212−1631225\frac{2}{12} - 16\frac{3}{12}
A common denominator of 12 is needed to perform the subtraction between the fractional parts.
3
Borrow 1 from the whole number 25 to perform the subtraction.
241412−16312=8111224\frac{14}{12} - 16\frac{3}{12} = 8\frac{11}{12} yards
Since 312\frac{3}{12} is larger than 212\frac{2}{12}, you must borrow a whole (1212\frac{12}{12}) to complete the operation.

Key Concept

Adding and subtracting mixed numbers with unlike denominators, including the borrowing method.
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Topics

Fraction Operations

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