To find out how much pasta Colin has left after using some for dinner, we need to subtract the amount he used from the total amount he had.
Colin starts with: \[ 8 \frac{2}{3} \text{ cups} \]
He uses: \[ 2 \frac{1}{2} \text{ cups} \]
First, we convert both mixed numbers to improper fractions.
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Convert \( 8 \frac{2}{3} \):
\[ 8 \frac{2}{3} = 8 \times 3 + 2 = 24 + 2 = 26 \quad \text{(numerator)} \] So, \[ 8 \frac{2}{3} = \frac{26}{3} \]
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Convert \( 2 \frac{1}{2} \):
\[ 2 \frac{1}{2} = 2 \times 2 + 1 = 4 + 1 = 5 \quad \text{(numerator)} \] So, \[ 2 \frac{1}{2} = \frac{5}{2} \]
Next, we need to subtract \( \frac{5}{2} \) from \( \frac{26}{3} \). To do this, we need a common denominator. The least common multiple (LCM) of 3 and 2 is 6.
We convert both fractions:
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Convert \( \frac{26}{3} \) to a denominator of 6:
\[ \frac{26}{3} = \frac{26 \times 2}{3 \times 2} = \frac{52}{6} \]
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Convert \( \frac{5}{2} \) to a denominator of 6:
\[ \frac{5}{2} = \frac{5 \times 3}{2 \times 3} = \frac{15}{6} \]
Now we can subtract the two fractions:
\[ \frac{52}{6} - \frac{15}{6} = \frac{52 - 15}{6} = \frac{37}{6} \]
Now, we convert \( \frac{37}{6} \) back to a mixed number:
- Divide 37 by 6. The quotient is 6 and the remainder is 1.
So, \[ \frac{37}{6} = 6 \frac{1}{6} \]
Thus, the amount of pasta Colin has left is:
\[ \boxed{6 \frac{1}{6}} \]
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