To find out how much fabric Sabrina has left after using some for her sewing projects, we start with the total amount of fabric she has and then subtract the amounts she used.
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Total fabric she has:
\( 2 \frac{2}{3} \) feet can be converted to an improper fraction. \[ 2 \frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3} \text{ feet} \] -
Amount used for the first project:
She used \( \frac{1}{2} \) foot. -
Amount used for the second project:
She used \( 1 \frac{3}{4} \) feet, which can also be converted to an improper fraction. \[ 1 \frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4} \text{ feet} \] -
Total amount used:
To find the total used, we need a common denominator for \( \frac{1}{2} \) and \( \frac{7}{4} \). The least common multiple of \( 2 \) and \( 4 \) is \( 4 \).Convert \( \frac{1}{2} \) to an equivalent fraction with a denominator of \( 4 \): \[ \frac{1}{2} = \frac{2}{4} \]
Now we add \( \frac{2}{4} \) and \( \frac{7}{4} \): \[ \frac{2}{4} + \frac{7}{4} = \frac{2 + 7}{4} = \frac{9}{4} \text{ feet} \]
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Calculate the leftover fabric:
Subtract the total used from the total fabric: \[ \frac{8}{3} - \frac{9}{4} \]To subtract these fractions, we need a common denominator, which is \( 12 \):
- Convert \( \frac{8}{3} \) to have a denominator of 12: \[ \frac{8}{3} = \frac{8 \times 4}{3 \times 4} = \frac{32}{12} \]
- Convert \( \frac{9}{4} \) to have a denominator of 12: \[ \frac{9}{4} = \frac{9 \times 3}{4 \times 3} = \frac{27}{12} \]
Now we subtract: \[ \frac{32}{12} - \frac{27}{12} = \frac{32 - 27}{12} = \frac{5}{12} \text{ feet} \]
Thus, Sabrina has \( \frac{5}{12} \) feet of fabric left after completing her sewing projects.