Solve 5/3-3/4/frac{11{12}}div6/5-frac{1}{5}

$$\frac { \frac { 5 } { 3 } - \frac { 3 } { 4 } } { \frac { 11 } { 12 } } \div \frac { 6 } { 5 } - \frac { 1 } { 5 }$$

Evaluate

$$\frac{19}{30}\approx 0.633333333$$

Solution Steps

Divide \frac{\frac{5}{3}-\frac{3}{4}}{\frac{11}{12}} by \frac{6}{5} by multiplying \frac{\frac{5}{3}-\frac{3}{4}}{\frac{11}{12}} by the reciprocal of \frac{6}{5}.

$$\frac{\left(\frac{5}{3}-\frac{3}{4}\right)\times 5}{\frac{11}{12}\times 6}-\frac{1}{5}$$

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

$$\frac{\left(\frac{20}{12}-\frac{9}{12}\right)\times 5}{\frac{11}{12}\times 6}-\frac{1}{5}$$

Since \frac{20}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{20-9}{12}\times 5}{\frac{11}{12}\times 6}-\frac{1}{5}$$

Subtract 9 from 20 to get 11.

$$\frac{\frac{11}{12}\times 5}{\frac{11}{12}\times 6}-\frac{1}{5}$$

Express \frac{11}{12}\times 5 as a single fraction.

$$\frac{\frac{11\times 5}{12}}{\frac{11}{12}\times 6}-\frac{1}{5}$$

Multiply 11 and 5 to get 55.

$$\frac{\frac{55}{12}}{\frac{11}{12}\times 6}-\frac{1}{5}$$

Express \frac{11}{12}\times 6 as a single fraction.

$$\frac{\frac{55}{12}}{\frac{11\times 6}{12}}-\frac{1}{5}$$

Multiply 11 and 6 to get 66.

$$\frac{\frac{55}{12}}{\frac{66}{12}}-\frac{1}{5}$$

Reduce the fraction \frac{66}{12} to lowest terms by extracting and canceling out 6.

$$\frac{\frac{55}{12}}{\frac{11}{2}}-\frac{1}{5}$$

Divide \frac{55}{12} by \frac{11}{2} by multiplying \frac{55}{12} by the reciprocal of \frac{11}{2}.

$$\frac{55}{12}\times \frac{2}{11}-\frac{1}{5}$$

Multiply \frac{55}{12} times \frac{2}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{55\times 2}{12\times 11}-\frac{1}{5}$$

Do the multiplications in the fraction \frac{55\times 2}{12\times 11}.

$$\frac{110}{132}-\frac{1}{5}$$

Reduce the fraction \frac{110}{132} to lowest terms by extracting and canceling out 22.

$$\frac{5}{6}-\frac{1}{5}$$

Least common multiple of 6 and 5 is 30. Convert \frac{5}{6} and \frac{1}{5} to fractions with denominator 30.

$$\frac{25}{30}-\frac{6}{30}$$

Since \frac{25}{30} and \frac{6}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-6}{30}$$

Subtract 6 from 25 to get 19.

$$\frac{19}{30}$$

Factor

$$\frac{19}{2 \cdot 3 \cdot 5} = 0.6333333333333333$$