Solve 1/3*2/3div((5/6-3/4)+(frac{6}{7}+frac{7}{8}))

$$\frac{ 1 }{ 3 } \times \frac{ 2 }{ 3 } \div (( \frac{ 5 }{ 6 } - \frac{ 3 }{ 4 } )+( \frac{ 6 }{ 7 } + \frac{ 7 }{ 8 } ))$$

Evaluate

$$\frac{112}{915}\approx 0.122404372$$

Solution Steps

Multiply \frac{1}{3} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1\times 2}{3\times 3}}{\frac{5}{6}-\frac{3}{4}+\frac{6}{7}+\frac{7}{8}}$$

Do the multiplications in the fraction \frac{1\times 2}{3\times 3}.

$$\frac{\frac{2}{9}}{\frac{5}{6}-\frac{3}{4}+\frac{6}{7}+\frac{7}{8}}$$

Least common multiple of 6 and 4 is 12. Convert \frac{5}{6} and \frac{3}{4} to fractions with denominator 12.

$$\frac{\frac{2}{9}}{\frac{10}{12}-\frac{9}{12}+\frac{6}{7}+\frac{7}{8}}$$

Since \frac{10}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2}{9}}{\frac{10-9}{12}+\frac{6}{7}+\frac{7}{8}}$$

Subtract 9 from 10 to get 1.

$$\frac{\frac{2}{9}}{\frac{1}{12}+\frac{6}{7}+\frac{7}{8}}$$

Least common multiple of 12 and 7 is 84. Convert \frac{1}{12} and \frac{6}{7} to fractions with denominator 84.

$$\frac{\frac{2}{9}}{\frac{7}{84}+\frac{72}{84}+\frac{7}{8}}$$

Since \frac{7}{84} and \frac{72}{84} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2}{9}}{\frac{7+72}{84}+\frac{7}{8}}$$

Add 7 and 72 to get 79.

$$\frac{\frac{2}{9}}{\frac{79}{84}+\frac{7}{8}}$$

Least common multiple of 84 and 8 is 168. Convert \frac{79}{84} and \frac{7}{8} to fractions with denominator 168.

$$\frac{\frac{2}{9}}{\frac{158}{168}+\frac{147}{168}}$$

Since \frac{158}{168} and \frac{147}{168} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2}{9}}{\frac{158+147}{168}}$$

Add 158 and 147 to get 305.

$$\frac{\frac{2}{9}}{\frac{305}{168}}$$

Divide \frac{2}{9} by \frac{305}{168} by multiplying \frac{2}{9} by the reciprocal of \frac{305}{168}.

$$\frac{2}{9}\times \frac{168}{305}$$

Multiply \frac{2}{9} times \frac{168}{305} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 168}{9\times 305}$$

Do the multiplications in the fraction \frac{2\times 168}{9\times 305}.

$$\frac{336}{2745}$$

Reduce the fraction \frac{336}{2745} to lowest terms by extracting and canceling out 3.

$$\frac{112}{915}$$

Factor

$$\frac{2 ^ {4} \cdot 7}{3 \cdot 5 \cdot 61} = 0.12240437158469945$$