QuestionAugust 27, 2025

Evaluate. ((2)/(3)+(1)/(4))cdot (6)/(7) Write your answer in simplest form. square

Evaluate. ((2)/(3)+(1)/(4))cdot (6)/(7) Write your answer in simplest form. square
Evaluate. ((2)/(3)+(1)/(4))cdot (6)/(7) Write your answer in simplest form. square

Solution
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Answer

\frac{11}{14} Explanation 1. Add fractions Convert \frac{2}{3} and \frac{1}{4} to a common denominator. The least common denominator is 12. \frac{2}{3} = \frac{8}{12}, \frac{1}{4} = \frac{3}{12}. Add them: \frac{8}{12} + \frac{3}{12} = \frac{11}{12}. 2. Multiply the result by \frac{6}{7} Multiply \frac{11}{12} by \frac{6}{7}: \frac{11}{12} \cdot \frac{6}{7} = \frac{11 \times 6}{12 \times 7} = \frac{66}{84}. 3. Simplify the fraction Simplify \frac{66}{84} by dividing both numerator and denominator by their greatest common divisor, which is 6: \frac{66 \div 6}{84 \div 6} = \frac{11}{14}.

Explanation

1. Add fractions<br /> Convert $\frac{2}{3}$ and $\frac{1}{4}$ to a common denominator. The least common denominator is 12. <br />$\frac{2}{3} = \frac{8}{12}$, $\frac{1}{4} = \frac{3}{12}$.<br />Add them: $\frac{8}{12} + \frac{3}{12} = \frac{11}{12}$.<br /><br />2. Multiply the result by $\frac{6}{7}$<br /> Multiply $\frac{11}{12}$ by $\frac{6}{7}$: <br />$\frac{11}{12} \cdot \frac{6}{7} = \frac{11 \times 6}{12 \times 7} = \frac{66}{84}$.<br /><br />3. Simplify the fraction<br /> Simplify $\frac{66}{84}$ by dividing both numerator and denominator by their greatest common divisor, which is 6:<br />$\frac{66 \div 6}{84 \div 6} = \frac{11}{14}$.
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