Question

seven students cut $5\frac{3}{4}$ inches of thread from a spool for a school project. what number represents the change in the amount of the thread on the spool?
\bigcirc\\ -$40\frac{1}{4}$ inches
\bigcirc\\ -$36\frac{3}{4}$ inches
\bigcirc\\ -$29\frac{3}{4}$ inches

Explanation:

Step1: Convert mixed number to improper fraction

The length of thread each student cuts is \(5\frac{3}{4}\) inches. Convert this to an improper fraction: \(5\frac{3}{4}=\frac{5\times4 + 3}{4}=\frac{23}{4}\) inches.

Step2: Calculate total length cut by 7 students

Multiply the length per student by the number of students: \(7\times\frac{23}{4}=\frac{161}{4}\) inches.

Step3: Convert back to mixed number

Convert \(\frac{161}{4}\) to a mixed number: \(161\div4 = 40\) with a remainder of \(1\), so \(\frac{161}{4}=40\frac{1}{4}\) inches. Since the thread is being removed from the spool, the change is negative, so it's \(-40\frac{1}{4}\) inches.

Answer:

A. \(-40\frac{1}{4}\) inches