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)
Responses
512 ft.
Start Fraction 5 over 12 End Fraction ft.
123 ft.
1 Start Fraction 2 over 3 End Fraction ft.
1 ft.
1 ft.
214 ft.
To find out how much fabric Shani has left, we need to subtract the lengths of the two projects she used fabric for from the original length of the fabric.
Length used for one sewing project: 1/2 ft
Length used for another sewing project: 1 3/4 ft
Total length used: 1/2 + 1 3/4
To add the fractions, we first need to convert the whole number 1 to a fraction with the same denominator:
1 = 4/4
So, 1 3/4 = 4/4 + 3/4 = 7/4
Adding the fractions: 1/2 + 7/4
To add the fractions, we need to find a common denominator, which is 4.
1/2 = 2/4
So, the sum is: 2/4 + 7/4 = 9/4
Now, we can subtract the total length used from the original length:
The original length is 2 2/3 ft, which we can convert to a mixed number: 2 2/3 = 8/3
Subtracting: 8/3 - 9/4
To subtract the fractions, we need to find a common denominator, which is 12.
8/3 = 32/12
9/4 = 27/12
So, the difference is: 32/12 - 27/12 = 5/12
The remaining fabric is 5/12 ft.
Therefore, the answer is: Start Fraction 5 over 12 End Fraction ft.