A piece of pipe is $303 / 4$ inches long. If five pieces, each $41 / 3$ inches long, are cut from the pipe, how many inches of pipe remain?
A) $263 / 4$ inches
B) $93 / 4$ inches
C) $9 \frac{1}{12}$ inches
D) $26 \frac{5}{12}$ inches
Answer (1)
Convert the mixed numbers to improper fractions: 30 4 3 = 4 123 and 4 3 1 = 3 13 .
Calculate the total length of the five pieces: 5 \t × 3 13 = 3 65 .
Subtract the total length of the cut pieces from the initial length: 4 123 − 3 65 = 12 109 .
Convert the improper fraction back to a mixed number: 12 109 = 9 12 1 . The remaining length is 9 12 1 inches.
Explanation
Problem Analysis We are given a pipe of length 30 4 3 inches. We need to cut five pieces of length 4 3 1 inches each and find the remaining length of the pipe.
Convert to Improper Fractions First, convert the mixed numbers to improper fractions: 30 4 3 = 4 30 × 4 + 3 = 4 120 + 3 = 4 123 inches 4 3 1 = 3 4 × 3 + 1 = 3 12 + 1 = 3 13 inches
Calculate Total Cut Length Next, calculate the total length of the five pieces: 5 × 4 3 1 = 5 × 3 13 = 3 5 × 13 = 3 65 inches
Subtract to Find Remaining Length Now, subtract the total length of the cut pieces from the initial length of the pipe: 4 123 − 3 65 = 4 × 3 123 × 3 − 3 × 4 65 × 4 = 12 369 − 12 260 = 12 369 − 260 = 12 109 inches
Convert Back to Mixed Number Finally, convert the improper fraction back to a mixed number: 12 109 = 9 12 1 inches
Final Answer The remaining length of the pipe is 9 12 1 inches.
Examples
This type of problem is useful in various real-life scenarios, such as carpentry, tailoring, or any situation where you need to cut pieces from a larger object. For example, imagine you are building a bookshelf and need to cut several shelves of equal length from a long piece of wood. Calculating the remaining length helps you ensure you have enough material for other parts of the project and minimize waste. Understanding fractions and mixed numbers is crucial for accurate measurements and efficient resource management in these practical applications.
