Solve 3/2-2/3/frac{3{4}+4/3}*frac{frac{7}{6}+frac{4}{3}}{frac{3}{5}-frac{5}{3}}

$$\frac { \frac { 3 } { 2 } - \frac { 2 } { 3 } } { \frac { 3 } { 4 } + \frac { 4 } { 3 } } \times \frac { \frac { 7 } { 6 } + \frac { 4 } { 3 } } { \frac { 3 } { 5 } - \frac { 5 } { 3 } }$$

Evaluate

$$-\frac{15}{16}=-0.9375$$

Solution Steps

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

$$\frac{\frac{9}{6}-\frac{4}{6}}{\frac{3}{4}+\frac{4}{3}}\times \frac{\frac{7}{6}+\frac{4}{3}}{\frac{3}{5}-\frac{5}{3}}$$

Since \frac{9}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9-4}{6}}{\frac{3}{4}+\frac{4}{3}}\times \frac{\frac{7}{6}+\frac{4}{3}}{\frac{3}{5}-\frac{5}{3}}$$

Subtract 4 from 9 to get 5.

$$\frac{\frac{5}{6}}{\frac{3}{4}+\frac{4}{3}}\times \frac{\frac{7}{6}+\frac{4}{3}}{\frac{3}{5}-\frac{5}{3}}$$

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

$$\frac{\frac{5}{6}}{\frac{9}{12}+\frac{16}{12}}\times \frac{\frac{7}{6}+\frac{4}{3}}{\frac{3}{5}-\frac{5}{3}}$$

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

$$\frac{\frac{5}{6}}{\frac{9+16}{12}}\times \frac{\frac{7}{6}+\frac{4}{3}}{\frac{3}{5}-\frac{5}{3}}$$

Add 9 and 16 to get 25.

$$\frac{\frac{5}{6}}{\frac{25}{12}}\times \frac{\frac{7}{6}+\frac{4}{3}}{\frac{3}{5}-\frac{5}{3}}$$

Divide \frac{5}{6} by \frac{25}{12} by multiplying \frac{5}{6} by the reciprocal of \frac{25}{12}.

$$\frac{5}{6}\times \frac{12}{25}\times \frac{\frac{7}{6}+\frac{4}{3}}{\frac{3}{5}-\frac{5}{3}}$$

Multiply \frac{5}{6} times \frac{12}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 12}{6\times 25}\times \frac{\frac{7}{6}+\frac{4}{3}}{\frac{3}{5}-\frac{5}{3}}$$

Do the multiplications in the fraction \frac{5\times 12}{6\times 25}.

$$\frac{60}{150}\times \frac{\frac{7}{6}+\frac{4}{3}}{\frac{3}{5}-\frac{5}{3}}$$

Reduce the fraction \frac{60}{150} to lowest terms by extracting and canceling out 30.

$$\frac{2}{5}\times \frac{\frac{7}{6}+\frac{4}{3}}{\frac{3}{5}-\frac{5}{3}}$$

Least common multiple of 6 and 3 is 6. Convert \frac{7}{6} and \frac{4}{3} to fractions with denominator 6.

$$\frac{2}{5}\times \frac{\frac{7}{6}+\frac{8}{6}}{\frac{3}{5}-\frac{5}{3}}$$

Since \frac{7}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$\frac{2}{5}\times \frac{\frac{7+8}{6}}{\frac{3}{5}-\frac{5}{3}}$$

Add 7 and 8 to get 15.

$$\frac{2}{5}\times \frac{\frac{15}{6}}{\frac{3}{5}-\frac{5}{3}}$$

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

$$\frac{2}{5}\times \frac{\frac{5}{2}}{\frac{3}{5}-\frac{5}{3}}$$

Least common multiple of 5 and 3 is 15. Convert \frac{3}{5} and \frac{5}{3} to fractions with denominator 15.

$$\frac{2}{5}\times \frac{\frac{5}{2}}{\frac{9}{15}-\frac{25}{15}}$$

Since \frac{9}{15} and \frac{25}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{5}\times \frac{\frac{5}{2}}{\frac{9-25}{15}}$$

Subtract 25 from 9 to get -16.

$$\frac{2}{5}\times \frac{\frac{5}{2}}{-\frac{16}{15}}$$

Divide \frac{5}{2} by -\frac{16}{15} by multiplying \frac{5}{2} by the reciprocal of -\frac{16}{15}.

$$\frac{2}{5}\times \frac{5}{2}\left(-\frac{15}{16}\right)$$

Multiply \frac{5}{2} times -\frac{15}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{5}\times \frac{5\left(-15\right)}{2\times 16}$$

Do the multiplications in the fraction \frac{5\left(-15\right)}{2\times 16}.

$$\frac{2}{5}\times \frac{-75}{32}$$

Fraction \frac{-75}{32} can be rewritten as -\frac{75}{32} by extracting the negative sign.

$$\frac{2}{5}\left(-\frac{75}{32}\right)$$

Multiply \frac{2}{5} times -\frac{75}{32} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(-75\right)}{5\times 32}$$

Do the multiplications in the fraction \frac{2\left(-75\right)}{5\times 32}.

$$\frac{-150}{160}$$

Reduce the fraction \frac{-150}{160} to lowest terms by extracting and canceling out 10.

$$-\frac{15}{16}$$

Factor

$$-\frac{15}{16} = -0.9375$$