Solve 1-1/4/frac{3{4}-11/3}-3frac{1/6-frac{2}{3}}{frac{1}{6}}

$$\frac { 1 - \frac { 1 } { 4 } } { \frac { 3 } { 4 } - 1 \frac { 1 } { 3 } } - \frac { 3 \frac { 1 } { 6 } - \frac { 2 } { 3 } } { \frac { 1 } { 6 } }$$

Evaluate

$$-\frac{114}{7}\approx -16.285714286$$

Solution Steps

Convert 1 to fraction \frac{4}{4}.

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

Since \frac{4}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 4 to get 3.

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

Multiply 1 and 3 to get 3.

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

Add 3 and 1 to get 4.

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

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

$$\frac{\frac{3}{4}}{\frac{9}{12}-\frac{16}{12}}-\frac{\frac{3\times 6+1}{6}-\frac{2}{3}}{\frac{1}{6}}$$

Since \frac{9}{12} and \frac{16}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3}{4}}{\frac{9-16}{12}}-\frac{\frac{3\times 6+1}{6}-\frac{2}{3}}{\frac{1}{6}}$$

Subtract 16 from 9 to get -7.

$$\frac{\frac{3}{4}}{-\frac{7}{12}}-\frac{\frac{3\times 6+1}{6}-\frac{2}{3}}{\frac{1}{6}}$$

Divide \frac{3}{4} by -\frac{7}{12} by multiplying \frac{3}{4} by the reciprocal of -\frac{7}{12}.

$$\frac{3}{4}\left(-\frac{12}{7}\right)-\frac{\frac{3\times 6+1}{6}-\frac{2}{3}}{\frac{1}{6}}$$

Multiply \frac{3}{4} times -\frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\left(-12\right)}{4\times 7}-\frac{\frac{3\times 6+1}{6}-\frac{2}{3}}{\frac{1}{6}}$$

Do the multiplications in the fraction \frac{3\left(-12\right)}{4\times 7}.

$$\frac{-36}{28}-\frac{\frac{3\times 6+1}{6}-\frac{2}{3}}{\frac{1}{6}}$$

Reduce the fraction \frac{-36}{28} to lowest terms by extracting and canceling out 4.

$$-\frac{9}{7}-\frac{\frac{3\times 6+1}{6}-\frac{2}{3}}{\frac{1}{6}}$$

Multiply 3 and 6 to get 18.

$$-\frac{9}{7}-\frac{\frac{18+1}{6}-\frac{2}{3}}{\frac{1}{6}}$$

Add 18 and 1 to get 19.

$$-\frac{9}{7}-\frac{\frac{19}{6}-\frac{2}{3}}{\frac{1}{6}}$$

Least common multiple of 6 and 3 is 6. Convert \frac{19}{6} and \frac{2}{3} to fractions with denominator 6.

$$-\frac{9}{7}-\frac{\frac{19}{6}-\frac{4}{6}}{\frac{1}{6}}$$

Since \frac{19}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{9}{7}-\frac{\frac{19-4}{6}}{\frac{1}{6}}$$

Subtract 4 from 19 to get 15.

$$-\frac{9}{7}-\frac{\frac{15}{6}}{\frac{1}{6}}$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

$$-\frac{9}{7}-\frac{\frac{5}{2}}{\frac{1}{6}}$$

Divide \frac{5}{2} by \frac{1}{6} by multiplying \frac{5}{2} by the reciprocal of \frac{1}{6}.

$$-\frac{9}{7}-\frac{5}{2}\times 6$$

Express \frac{5}{2}\times 6 as a single fraction.

$$-\frac{9}{7}-\frac{5\times 6}{2}$$

Multiply 5 and 6 to get 30.

$$-\frac{9}{7}-\frac{30}{2}$$

Divide 30 by 2 to get 15.

$$-\frac{9}{7}-15$$

Convert 15 to fraction \frac{105}{7}.

$$-\frac{9}{7}-\frac{105}{7}$$

Since -\frac{9}{7} and \frac{105}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-9-105}{7}$$

Subtract 105 from -9 to get -114.

$$-\frac{114}{7}$$

Factor

$$-\frac{114}{7} = -16\frac{2}{7} = -16.285714285714285$$