Solve 21/10+4/5*1/12/frac{3{2}div(frac{3}{4}-frac{5}{2})}

$$\frac { \frac { 21 } { 10 } + \frac { 4 } { 5 } * \frac { 1 } { 12 } } { \frac { 3 } { 2 } \div ( \frac { 3 } { 4 } - \frac { 5 } { 2 } ) }$$

Evaluate

$$-\frac{91}{36}\approx -2.527777778$$

Solution Steps

Multiply \frac{4}{5} times \frac{1}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{21}{10}+\frac{4\times 1}{5\times 12}}{\frac{\frac{3}{2}}{\frac{3}{4}-\frac{5}{2}}}$$

Do the multiplications in the fraction \frac{4\times 1}{5\times 12}.

$$\frac{\frac{21}{10}+\frac{4}{60}}{\frac{\frac{3}{2}}{\frac{3}{4}-\frac{5}{2}}}$$

Reduce the fraction \frac{4}{60} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{21}{10}+\frac{1}{15}}{\frac{\frac{3}{2}}{\frac{3}{4}-\frac{5}{2}}}$$

Least common multiple of 10 and 15 is 30. Convert \frac{21}{10} and \frac{1}{15} to fractions with denominator 30.

$$\frac{\frac{63}{30}+\frac{2}{30}}{\frac{\frac{3}{2}}{\frac{3}{4}-\frac{5}{2}}}$$

Since \frac{63}{30} and \frac{2}{30} have the same denominator, add them by adding their numerators.

$$\frac{\frac{63+2}{30}}{\frac{\frac{3}{2}}{\frac{3}{4}-\frac{5}{2}}}$$

Add 63 and 2 to get 65.

$$\frac{\frac{65}{30}}{\frac{\frac{3}{2}}{\frac{3}{4}-\frac{5}{2}}}$$

Reduce the fraction \frac{65}{30} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{13}{6}}{\frac{\frac{3}{2}}{\frac{3}{4}-\frac{5}{2}}}$$

Least common multiple of 4 and 2 is 4. Convert \frac{3}{4} and \frac{5}{2} to fractions with denominator 4.

$$\frac{\frac{13}{6}}{\frac{\frac{3}{2}}{\frac{3}{4}-\frac{10}{4}}}$$

Since \frac{3}{4} and \frac{10}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{13}{6}}{\frac{\frac{3}{2}}{\frac{3-10}{4}}}$$

Subtract 10 from 3 to get -7.

$$\frac{\frac{13}{6}}{\frac{\frac{3}{2}}{-\frac{7}{4}}}$$

Divide \frac{3}{2} by -\frac{7}{4} by multiplying \frac{3}{2} by the reciprocal of -\frac{7}{4}.

$$\frac{\frac{13}{6}}{\frac{3}{2}\left(-\frac{4}{7}\right)}$$

Multiply \frac{3}{2} times -\frac{4}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{13}{6}}{\frac{3\left(-4\right)}{2\times 7}}$$

Do the multiplications in the fraction \frac{3\left(-4\right)}{2\times 7}.

$$\frac{\frac{13}{6}}{\frac{-12}{14}}$$

Reduce the fraction \frac{-12}{14} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{13}{6}}{-\frac{6}{7}}$$

Divide \frac{13}{6} by -\frac{6}{7} by multiplying \frac{13}{6} by the reciprocal of -\frac{6}{7}.

$$\frac{13}{6}\left(-\frac{7}{6}\right)$$

Multiply \frac{13}{6} times -\frac{7}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\left(-7\right)}{6\times 6}$$

Do the multiplications in the fraction \frac{13\left(-7\right)}{6\times 6}.

$$\frac{-91}{36}$$

Fraction \frac{-91}{36} can be rewritten as -\frac{91}{36} by extracting the negative sign.

$$-\frac{91}{36}$$

Factor

$$-\frac{91}{36} = -2\frac{19}{36} = -2.5277777777777777$$