Solve 1/2+1/7/frac{1{2}-1/7}left(frac{2}{3}+frac{21}{24}right)9^-2

$$\frac{ \frac{ 1 }{ 2 } + \frac{ 1 }{ 7 } }{ \frac{ 1 }{ 2 } - \frac{ 1 }{ 7 } } \left( \frac{ 2 }{ 3 } + \frac{ 21 }{ 24 } \right) { 9 }^{ -2 }$$

Evaluate

$$\frac{37}{1080}\approx 0.034259259$$

Solution Steps

Add \frac{1}{2} and \frac{1}{7} to get \frac{9}{14}.

$$\frac{\frac{9}{14}}{\frac{1}{2}-\frac{1}{7}}\left(\frac{2}{3}+\frac{21}{24}\right)\times 9^{-2}$$

Subtract \frac{1}{7} from \frac{1}{2} to get \frac{5}{14}.

$$\frac{\frac{9}{14}}{\frac{5}{14}}\left(\frac{2}{3}+\frac{21}{24}\right)\times 9^{-2}$$

Divide \frac{9}{14} by \frac{5}{14} by multiplying \frac{9}{14} by the reciprocal of \frac{5}{14}.

$$\frac{9}{14}\times \frac{14}{5}\left(\frac{2}{3}+\frac{21}{24}\right)\times 9^{-2}$$

Multiply \frac{9}{14} and \frac{14}{5} to get \frac{9}{5}.

$$\frac{9}{5}\left(\frac{2}{3}+\frac{21}{24}\right)\times 9^{-2}$$

Reduce the fraction \frac{21}{24} to lowest terms by extracting and canceling out 3.

$$\frac{9}{5}\left(\frac{2}{3}+\frac{7}{8}\right)\times 9^{-2}$$

Add \frac{2}{3} and \frac{7}{8} to get \frac{37}{24}.

$$\frac{9}{5}\times \frac{37}{24}\times 9^{-2}$$

Multiply \frac{9}{5} and \frac{37}{24} to get \frac{111}{40}.

$$\frac{111}{40}\times 9^{-2}$$

Calculate 9 to the power of -2 and get \frac{1}{81}.

$$\frac{111}{40}\times \frac{1}{81}$$

Multiply \frac{111}{40} and \frac{1}{81} to get \frac{37}{1080}.

$$\frac{37}{1080}$$

Factor

$$\frac{37}{2 ^ {3} \cdot 3 ^ {3} \cdot 5} = 0.03425925925925926$$