Solve 5/12/6-frac{7{18}-11/8}

$$\frac{ \frac{ 5 }{ 12 } }{ 6- \frac{ 7 }{ 18 } - \frac{ 11 }{ 8 } }$$

Evaluate

$$\frac{6}{61}\approx 0.098360656$$

Solution Steps

Convert 6 to fraction \frac{108}{18}.

$$\frac{\frac{5}{12}}{\frac{108}{18}-\frac{7}{18}-\frac{11}{8}}$$

Since \frac{108}{18} and \frac{7}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{12}}{\frac{108-7}{18}-\frac{11}{8}}$$

Subtract 7 from 108 to get 101.

$$\frac{\frac{5}{12}}{\frac{101}{18}-\frac{11}{8}}$$

Least common multiple of 18 and 8 is 72. Convert \frac{101}{18} and \frac{11}{8} to fractions with denominator 72.

$$\frac{\frac{5}{12}}{\frac{404}{72}-\frac{99}{72}}$$

Since \frac{404}{72} and \frac{99}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{12}}{\frac{404-99}{72}}$$

Subtract 99 from 404 to get 305.

$$\frac{\frac{5}{12}}{\frac{305}{72}}$$

Divide \frac{5}{12} by \frac{305}{72} by multiplying \frac{5}{12} by the reciprocal of \frac{305}{72}.

$$\frac{5}{12}\times \frac{72}{305}$$

Multiply \frac{5}{12} times \frac{72}{305} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 72}{12\times 305}$$

Do the multiplications in the fraction \frac{5\times 72}{12\times 305}.

$$\frac{360}{3660}$$

Reduce the fraction \frac{360}{3660} to lowest terms by extracting and canceling out 60.

$$\frac{6}{61}$$

Factor

$$\frac{2 \cdot 3}{61} = 0.09836065573770492$$