Solve 11/5left(1/3-1/2right)frac{3/11}{frac{5}{4}}

$$\frac{ \frac{ 11 }{ 5 } \left( \frac{ 1 }{ 3 } - \frac{ 1 }{ 2 } \right) \frac{ 3 }{ 11 } }{ \frac{ 5 }{ 4 } }$$

Evaluate

$$-\frac{2}{25}=-0.08$$

Solution Steps

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{\frac{11}{5}\left(\frac{2}{6}-\frac{3}{6}\right)\times \frac{3}{11}}{\frac{5}{4}}$$

Since \frac{2}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{11}{5}\times \frac{2-3}{6}\times \frac{3}{11}}{\frac{5}{4}}$$

Subtract 3 from 2 to get -1.

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

Multiply \frac{11}{5} times -\frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{11\left(-1\right)}{5\times 6}.

$$\frac{\frac{-11}{30}\times \frac{3}{11}}{\frac{5}{4}}$$

Fraction \frac{-11}{30} can be rewritten as -\frac{11}{30} by extracting the negative sign.

$$\frac{-\frac{11}{30}\times \frac{3}{11}}{\frac{5}{4}}$$

Multiply -\frac{11}{30} times \frac{3}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-11\times 3}{30\times 11}}{\frac{5}{4}}$$

Do the multiplications in the fraction \frac{-11\times 3}{30\times 11}.

$$\frac{\frac{-33}{330}}{\frac{5}{4}}$$

Reduce the fraction \frac{-33}{330} to lowest terms by extracting and canceling out 33.

$$\frac{-\frac{1}{10}}{\frac{5}{4}}$$

Divide -\frac{1}{10} by \frac{5}{4} by multiplying -\frac{1}{10} by the reciprocal of \frac{5}{4}.

$$-\frac{1}{10}\times \frac{4}{5}$$

Multiply -\frac{1}{10} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-4}{10\times 5}$$

Do the multiplications in the fraction \frac{-4}{10\times 5}.

$$\frac{-4}{50}$$

Reduce the fraction \frac{-4}{50} to lowest terms by extracting and canceling out 2.

$$-\frac{2}{25}$$

Factor

$$-\frac{2}{25} = -0.08$$