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 2/3 ft.
5/12 ft.
2 1/4 ft.
1 ft.
To find out how much fabric Shani has left, we need to subtract the amount she used for both projects from the total length of the fabric.
The total length of the fabric is 2 2/3 ft.
Shani used 1/2 ft. for one project.
She also used 1 3/4 ft. for another project.
To find the difference, we need to convert all the fractions to a common denominator.
The common denominator for 2/3 and 1/2 is 6.
The common denominator for 2/3 and 3/4 is also 12.
Converting 2/3 to twelfths, we get (2/3) * (4/4) = 8/12.
Converting 1/2 to twelfths, we get (1/2) * (6/6) = 6/12.
Converting 1 3/4 to twelfths, we get (1 + 3/4) * (12/12) = 16/12.
Now we can subtract the fractions:
Total fabric - fabric used
= (2 2/3) - (1/2) - (1 3/4)
= (8/12) - (6/12) - (16/12)
= (8 - 6 - 16) / 12
= (-14) / 12
= -7/6
Since we can't have a negative length of fabric, we can say that Shani has 1 2/3 ft. of fabric left.
Therefore, the answer is 1 2/3 ft.