A new section of freeway will be 8 1/2 mi long. During the first month of construction, 2 7/10 mi were built. During the second month, 3 3/5 mi were built. How many more miles were left to build?
You need to get commone denominators of 10ths first.
1/2 = 5/10 and 3/5 = 6/10
Add up the the two parts that were built and subtract from 8 5/10
Can you do it from here or do you need more help?
2 7/10 + 3 6/10 = 5 13/10 = 6 3/10
8 5/10 - 6 3/10 = ?
2 1/5
Right.
To find out how many more miles were left to build, we need to subtract the distance built during the first and second month from the total length of the freeway.
First, let's convert the mixed numbers to improper fractions:
8 1/2 = (8 * 2 + 1) / 2 = 17/2
2 7/10 = (2 * 10 + 7) / 10 = 27/10
3 3/5 = (3 * 5 + 3) / 5 = 18/5
Now, let's calculate the distance left to build:
Total length - Distance built in first month - Distance built in second month
Distance left to build = 17/2 - 27/10 - 18/5
To subtract these fractions, we need a common denominator. Since 2, 10, and 5 all divide evenly into 10, we can use 10 as our common denominator.
Distance left to build = (17/2)(5/5) - (27/10)(1/1) - (18/5)(2/2)
Distance left to build = 85/10 - 27/10 - 36/10
Distance left to build = (85 - 27 - 36)/10
Distance left to build = 22/10
Simplifying this fraction, we get:
Distance left to build = 11/5 or 2 1/5
Therefore, there were 2 1/5 miles left to build.