To find out how much shredded newspaper each person at the table received, we need to first determine the total amount of shredded newspaper that Cecilia and Juan brought, and then divide that total by the number of people (5).
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Convert the fractions to a common denominator:
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Cecilia had \( \frac{2}{3} \) pound of shredded newspaper. The denominator of 3 can be converted to 12, the least common multiple of 3 and 12.
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To convert \( \frac{2}{3} \) to twelfths: \[ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \]
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Juan had \( \frac{7}{12} \) pound of shredded newspaper, which does not need conversion.
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Add the fractions: Now we can add \( \frac{8}{12} \) and \( \frac{7}{12} \): \[ \frac{8}{12} + \frac{7}{12} = \frac{8 + 7}{12} = \frac{15}{12} \]
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Divide by the number of people: To find out how much shredded newspaper each person receives, divide the total by 5: \[ \text{Amount per person} = \frac{\frac{15}{12}}{5} \] This is the same as multiplying by the reciprocal of 5: \[ = \frac{15}{12} \times \frac{1}{5} = \frac{15}{60} \]
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Simplify the fraction: \[ \frac{15}{60} = \frac{1}{4} \]
Therefore, each person at the table received \( \frac{1}{4} \) pound of shredded newspaper.
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