Solve 5/4*16/7-44/5:frac{11/15}{frac{1}{3}-frac{5}{6}}=

$$\frac { \frac { 5 } { 4 } \cdot \frac { 16 } { 7 } - \frac { 44 } { 5 } : \frac { 11 } { 15 } } { \frac { 1 } { 3 } - \frac { 5 } { 6 } } =$$

Evaluate

$$\frac{128}{7}\approx 18.285714286$$

Solution Steps

Multiply \frac{5}{4} times \frac{16}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5\times 16}{4\times 7}-\frac{\frac{44}{5}}{\frac{11}{15}}}{\frac{1}{3}-\frac{5}{6}}$$

Do the multiplications in the fraction \frac{5\times 16}{4\times 7}.

$$\frac{\frac{80}{28}-\frac{\frac{44}{5}}{\frac{11}{15}}}{\frac{1}{3}-\frac{5}{6}}$$

Reduce the fraction \frac{80}{28} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{20}{7}-\frac{\frac{44}{5}}{\frac{11}{15}}}{\frac{1}{3}-\frac{5}{6}}$$

Divide \frac{44}{5} by \frac{11}{15} by multiplying \frac{44}{5} by the reciprocal of \frac{11}{15}.

$$\frac{\frac{20}{7}-\frac{44}{5}\times \frac{15}{11}}{\frac{1}{3}-\frac{5}{6}}$$

Multiply \frac{44}{5} times \frac{15}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{20}{7}-\frac{44\times 15}{5\times 11}}{\frac{1}{3}-\frac{5}{6}}$$

Do the multiplications in the fraction \frac{44\times 15}{5\times 11}.

$$\frac{\frac{20}{7}-\frac{660}{55}}{\frac{1}{3}-\frac{5}{6}}$$

Divide 660 by 55 to get 12.

$$\frac{\frac{20}{7}-12}{\frac{1}{3}-\frac{5}{6}}$$

Convert 12 to fraction \frac{84}{7}.

$$\frac{\frac{20}{7}-\frac{84}{7}}{\frac{1}{3}-\frac{5}{6}}$$

Since \frac{20}{7} and \frac{84}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{20-84}{7}}{\frac{1}{3}-\frac{5}{6}}$$

Subtract 84 from 20 to get -64.

$$\frac{-\frac{64}{7}}{\frac{1}{3}-\frac{5}{6}}$$

Least common multiple of 3 and 6 is 6. Convert \frac{1}{3} and \frac{5}{6} to fractions with denominator 6.

$$\frac{-\frac{64}{7}}{\frac{2}{6}-\frac{5}{6}}$$

Since \frac{2}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{64}{7}}{\frac{2-5}{6}}$$

Subtract 5 from 2 to get -3.

$$\frac{-\frac{64}{7}}{\frac{-3}{6}}$$

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

$$\frac{-\frac{64}{7}}{-\frac{1}{2}}$$

Divide -\frac{64}{7} by -\frac{1}{2} by multiplying -\frac{64}{7} by the reciprocal of -\frac{1}{2}.

$$-\frac{64}{7}\left(-2\right)$$

Express -\frac{64}{7}\left(-2\right) as a single fraction.

$$\frac{-64\left(-2\right)}{7}$$

Multiply -64 and -2 to get 128.

$$\frac{128}{7}$$

Factor

$$\frac{2 ^ {7}}{7} = 18\frac{2}{7} = 18.285714285714285$$