To find the weight of each textbook, we begin by dividing the total weight of the textbooks by the number of textbooks.
The total weight of the 5 textbooks is \( 6 \frac{2}{3} \) pounds. First, we need to convert this mixed number into an improper fraction.
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Convert \( 6 \frac{2}{3} \) into an improper fraction: \[ 6 \frac{2}{3} = \frac{6 \times 3 + 2}{3} = \frac{18 + 2}{3} = \frac{20}{3} \]
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Now, we will divide this fraction by the number of textbooks, which is 5: \[ \text{Weight of each book} = \frac{20/3}{5} \]
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Dividing by a whole number is the same as multiplying by the reciprocal: \[ \frac{20}{3} \div 5 = \frac{20}{3} \times \frac{1}{5} = \frac{20 \times 1}{3 \times 5} = \frac{20}{15} \]
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Now, we simplify \( \frac{20}{15} \): \[ \frac{20}{15} = \frac{4}{3} \]
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Finally, we convert \( \frac{4}{3} \) back into a mixed number: \[ \frac{4}{3} = 1 \frac{1}{3} \]
Thus, the weight of each textbook is \( \boxed{1 \frac{1}{3}} \) pounds.
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