Shani has a piece of fabric that is 2 2/3 ft. long. She uses 1/2 ft. for one sewing project and 1 3/4 ft. for another project. How much fabric does Shani have left? Solve this multi-step real-world problem. Express your answer in simplest form.(1 point)
1 ft.
1 2/3 ft.
5/12 ft.
2 1/4 ft.
To solve this problem, we need to subtract the amount of fabric used from the total amount of fabric that Shani had.
The total amount of fabric that Shani had is 2 2/3 ft.
The amount of fabric used for the first sewing project is 1/2 ft.
The amount of fabric used for the second sewing project is 1 3/4 ft.
To find how much fabric is left, we subtract the sum of the fabric used for both projects from the total amount of fabric that Shani had:
2 2/3 ft - (1/2 ft + 1 3/4 ft)
First, let's convert 2 2/3 ft into an improper fraction:
2 2/3 ft = (3*2 + 2)/3 ft = 6/3 + 2/3 ft = 8/3 ft
Now, let's add the fractions that represent the fabric used for both projects:
1/2 ft + 7/4 ft
To add fractions, we need to have a common denominator which is the least common multiple (LCM) of 2 and 4, which is 4.
1/2 ft = 2/4 ft (multiplying numerator and denominator by 2)
Now, we can add the fractions:
2/4 ft + 7/4 ft = 9/4 ft
Now, let's subtract the sum of the fabric used from the total amount of fabric that Shani had:
8/3 ft - 9/4 ft
To subtract fractions, we need to have a common denominator which is the least common multiple (LCM) of 3 and 4, which is 12.
8/3 ft = 32/12 ft (multiplying numerator and denominator by 4)
9/4 ft = 27/12 ft (multiplying numerator and denominator by 3)
Now we can subtract the fractions:
32/12 ft - 27/12 ft = (32 - 27)/12 ft = 5/12 ft
Therefore, Shani has 5/12 ft of fabric left.