A construction crew has just finished building a road. The road is
10 kilometers long. If the crew worked for
4 2/3 days, how many kilometers of road did they build each day? (Assume they built the same amount each day.)
Write your answer as a mixed number in simplest form.
10 / 4 2/3
10 / (14/3)
10 * (3/14) = 30/14 = 2 2/14 = 2 1/7
To find out how many kilometers of road the crew built each day, we need to divide the total length of the road by the number of days they worked.
Total length of road = 10 kilometers
Number of days worked = 4 2/3 days
To represent the number of days worked as an improper fraction, we can multiply the whole number (4) by the denominator of the fraction (3) and add the numerator (2) to get the total number of thirds.
4 * 3 = 12
12 + 2 = 14
So, the crew worked for a total of 14/3 days.
Now we can divide the total length of the road by the number of days worked:
10 / (14/3)
To divide by a fraction, we can multiply by its reciprocal:
10 * (3/14)
Simplifying the fraction:
(10 * 3) / 14 = 30/14
The fraction 30/14 can be simplified by finding the greatest common divisor (GCD) of the numerator (30) and the denominator (14), which is 2:
30/2 = 15
14/2 = 7
So, the simplified fraction is 15/7.
To write this as a mixed number, we divide the numerator (15) by the denominator (7) and express the quotient as a mixed number:
15 divided by 7 is 2 with a remainder of 1.
So, the crew built 2 1/7 kilometers of road each day.
To find out how many kilometers of road the construction crew built each day, we need to divide the total length of the road by the number of days they worked.
The total length of the road is 10 kilometers, and the crew worked for 4 2/3 days.
First, we need to convert the mixed number of days to an improper fraction:
4 2/3 = (4 * 3 + 2) / 3 = 14/3
Now, we can divide the total length of the road by the number of days:
10 km / (14/3) days
To divide by a fraction, we multiply by its reciprocal:
10 km * (3/14) days
Now, we can simplify the expression:
10 km * (3/14) days = 30/14 km
This can be simplified further by dividing both the numerator and denominator by their greatest common divisor, which is 2:
30/14 km = (15*2)/(7*2) km = 15/7 km
Therefore, the construction crew built 15/7 kilometers of road each day.