An upholsterer cuts a $1 \frac{6}{3}$ foot piece of cording from a piece that is $2 \frac{1}{4}$ feet long. How much cording is left?
A. $\frac{7}{12}$ ft
B. $1 \frac{5}{12}$ ft
C. $1 \frac{7}{12}$ ft
D. $3 \frac{11}{12}$ ft
Answer (1)
Convert the mixed numbers to improper fractions: 2 4 1 = 4 9 and 1 3 6 = 3 .
Subtract the lengths: 4 9 − 3 = 4 9 − 4 12 = − 4 3 .
Since the result is negative, consider the absolute value or assume a different problem statement.
If the cut piece was 1 3 2 instead, the remaining length would be 12 7 feet, matching option A. Therefore, the final answer is 12 7 .
Explanation
Understanding the Problem We are given that the initial length of the cording is 2 4 1 feet and a piece of length 1 3 6 feet is cut from it. We need to find the remaining length of the cording.
Converting to Improper Fractions First, convert the mixed numbers to improper fractions. We have:
2 4 1 = 4 2 × 4 + 1 = 4 8 + 1 = 4 9 feet
1 3 6 = 3 1 × 3 + 6 = 3 3 + 6 = 3 9 = 3 feet
Subtracting the Lengths Now, subtract the length of the cut piece from the initial length:
4 9 − 3 = 4 9 − 4 3 × 4 = 4 9 − 4 12 = 4 9 − 12 = 4 − 3 feet
Since we cannot have a negative length remaining, there must be an error in the problem statement. The length of the piece cut cannot be greater than the initial length. However, we can find the absolute value of the result to see how much shorter the remaining piece is compared to zero. The absolute value is 4 − 3 = 4 3 .
Addressing the Negative Result Since the result is negative, it means that the piece cut was longer than the original piece. However, if we assume that the question meant to ask how much shorter the original piece is than the piece that was cut, then the answer would be 4 3 feet. If the initial length was actually 2 4 1 and the piece cut was 1 3 2 , then the calculation would be: 2 4 1 − 1 3 2 = 4 9 − 3 5 = 12 27 − 12 20 = 12 7
Final Answer Given the options, the closest answer is 12 7 feet, which would be the correct answer if the piece cut was 1 3 2 instead of 1 3 6 .
Examples
In upholstery, calculating the remaining length of cording after cutting a piece is essential for efficient material usage and cost management. For instance, if you start with a 10-foot cord and use 3.5 feet for a chair, you need to know the remaining 6.5 feet to plan for other projects. Accurate calculations prevent waste and ensure you have enough material for each task. This skill is also useful in sewing, crafting, and any situation where precise measurements are needed to avoid shortages or overspending.
