(4) ((1)/(3)+(5)/(7)+(1)/(2))×(3)/(13)

Find Common Denominator: First, we need to add the fractions (1/3), (5/7), and (1/2). To do this, we need to find a common denominator, which is 42 (the least common multiple of 3, 7, and 2).Convert to Common Denominator: Now we convert each fraction to have the common denominator of 42: (1/3) becomes (14/42), (5/7) becomes (30/42), and (1/2) becomes (21/42).Add Fractions: Next, we add the fractions with the common denominator: (14/42) + (30/42) + (21/42) = (14 + 30 + 21)/42 = 65/42.Multiply by (3/13): Now we have the sum of the fractions, which is 65/42. We need to multiply this sum by (3/13).Simplify Fraction: We multiply the fractions (65/42) × (3/13) by multiplying the numerators together and the denominators together: (65 × 3)/(42 × 13) = 195/546.Final Answer: We can simplify the fraction 195/546 by dividing both the numerator and the denominator by their greatest common divisor, which is 3. 195 ÷ 3 = 65, and 546 ÷ 3 = 182.After simplification, we get the fraction 65/182. This is the final answer, as it cannot be simplified further.

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( $4$ ) $\left(\frac{1}{3}+\frac{5}{7}+\frac{1}{2}\right) \times \frac{3}{13}$

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Multiply and divide complex numbers

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\left(\frac{1}{3}+\frac{5}{7}+\frac{1}{2}\right) \times \frac{3}{13}

Find Common Denominator: First, we need to add the fractions $(\frac{1}{3}), (\frac{5}{7}),$ and $(\frac{1}{2})$ . To do this, we need to find a common denominator, which is $42$ (the least common multiple of $3$ , $7$ , and $2$ ).
Convert to Common Denominator: Now we convert each fraction to have the common denominator of $42$ : $(\frac{1}{3})$ becomes $(\frac{14}{42})$ , $(\frac{5}{7})$ becomes $(\frac{30}{42})$ , and $(\frac{1}{2})$ becomes $(\frac{21}{42})$ .
Add Fractions: Next, we add the fractions with the common denominator: $\frac{14}{42} + \frac{30}{42} + \frac{21}{42} = \frac{14 + 30 + 21}{42} = \frac{65}{42}$ .
Multiply by $(\frac{3}{13}):</b> Now we have the sum of the fractions, which is \$\frac{65}{42}$ . We need to multiply this sum by $(\frac{3}{13})$ .
Simplify Fraction: We multiply the fractions $(\frac{65}{42}) \times (\frac{3}{13})$ by multiplying the numerators together and the denominators together: $(65 \times 3)/(42 \times 13) = \frac{195}{546}$ .
Final Answer: We can simplify the fraction $\frac{195}{546}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $3$ . $\newline$ $195 \div 3 = 65$ , and $546 \div 3 = 182$ .
Final Answer: We can simplify the fraction $\frac{195}{546}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $3$ . $195 \div 3 = 65$ , and $546 \div 3 = 182$ . After simplification, we get the fraction $\frac{65}{182}$ . This is the final answer, as it cannot be simplified further.

( $4$ ) $\left(\frac{1}{3}+\frac{5}{7}+\frac{1}{2}\right) \times \frac{3}{13}$

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( $4$ ) $\left(\frac{1}{3}+\frac{5}{7}+\frac{1}{2}\right) \times \frac{3}{13}$