QuestionJuly 16, 2025

(1)/(3)(2(1)/(3)+6(1)/(2))-(7)/(24)

(1)/(3)(2(1)/(3)+6(1)/(2))-(7)/(24)
(1)/(3)(2(1)/(3)+6(1)/(2))-(7)/(24)

Solution
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Answer

\frac{191}{72} Explanation 1. Convert Mixed Numbers to Improper Fractions 2\frac{1}{3} = \frac{7}{3} and 6\frac{1}{2} = \frac{13}{2}. 2. Add the Improper Fractions Find a common denominator: \frac{7}{3} + \frac{13}{2} = \frac{14}{6} + \frac{39}{6} = \frac{53}{6}. 3. Multiply by \frac{1}{3} \frac{1}{3} \times \frac{53}{6} = \frac{53}{18}. 4. Subtract \frac{7}{24} Find a common denominator: \frac{53}{18} - \frac{7}{24} = \frac{212}{72} - \frac{21}{72} = \frac{191}{72}.

Explanation

1. Convert Mixed Numbers to Improper Fractions<br /> $2\frac{1}{3} = \frac{7}{3}$ and $6\frac{1}{2} = \frac{13}{2}$.<br />2. Add the Improper Fractions<br /> Find a common denominator: $\frac{7}{3} + \frac{13}{2} = \frac{14}{6} + \frac{39}{6} = \frac{53}{6}$.<br />3. Multiply by $\frac{1}{3}$<br /> $\frac{1}{3} \times \frac{53}{6} = \frac{53}{18}$.<br />4. Subtract $\frac{7}{24}$<br /> Find a common denominator: $\frac{53}{18} - \frac{7}{24} = \frac{212}{72} - \frac{21}{72} = \frac{191}{72}$.
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