A construction worker needs to cut a pipe that is 7 1/2 feet long into sections that are each 2 3/4 feet long. How many sections can be cut from the pipe?
To find out how many sections can be cut from the pipe, we need to divide the total length of the pipe by the length of each section.
First, let's convert the length of the pipe into a mixed number: 7 1/2 feet = 7 + 1/2 = 7 + 2/4 = 7 + 4/8 = 7 4/8 = 7 1/2.
Next, let's convert the length of each section into a mixed number: 2 3/4 feet = 2 + 3/4 = 2 + 6/8 = 2 6/8 = 2 3/4.
Now, let's divide the total length of the pipe by the length of each section: (7 1/2) / (2 3/4).
To simplify the division, let's change the mixed numbers to improper fractions: (15/2) / (11/4).
Next, let's invert the divisor and multiply: (15/2) * (4/11) = 60/22.
To simplify the fraction, let's find the greatest common divisor (GCD) of the numerator and denominator, which is 2: (60/2) / (22/2) = 30/11.
Therefore, the construction worker can cut 30 sections from the pipe, each measuring 2 3/4 feet long.