Question

topic 1 operating with rational numbers

1. eduardo needs to cut a 15-foot steel pipe into 2\frac{1}{3}-foot pieces. how many 2\frac{1}{3}-foot pieces can he cut from the pipe?

Explanation:

Step1: Convert mixed number to improper fraction

The length of each piece is \(2\frac{1}{3}\) feet. Convert this to an improper fraction: \(2\frac{1}{3}=\frac{2\times3 + 1}{3}=\frac{7}{3}\) feet. The total length of the pipe is 15 feet, which is \(\frac{15}{1}\) feet.

Step2: Divide total length by piece length

To find the number of pieces, divide the total length by the length of each piece: \(\frac{15}{1}\div\frac{7}{3}\). When dividing fractions, multiply by the reciprocal: \(\frac{15}{1}\times\frac{3}{7}=\frac{45}{7}\approx6.428\). Since we can't have a fraction of a piece, we take the whole number part.

Answer:

6