Solve (9/4+4/4)1/3/(frac{2{14}-frac{5}{7})div(1+frac{5}{6})}

$$\frac{ ( \frac{ 9 }{ 4 } + \frac{ 4 }{ 4 } ) \frac{ 1 }{ 3 } }{ ( \frac{ 2 }{ 14 } - \frac{ 5 }{ 7 } ) \div (1+ \frac{ 5 }{ 6 } ) }$$

Evaluate

$$-\frac{1001}{288}\approx -3.475694444$$

Solution Steps

Since \frac{9}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9+4}{4}\times \frac{1}{3}}{\frac{\frac{2}{14}-\frac{5}{7}}{1+\frac{5}{6}}}$$

Add 9 and 4 to get 13.

$$\frac{\frac{13}{4}\times \frac{1}{3}}{\frac{\frac{2}{14}-\frac{5}{7}}{1+\frac{5}{6}}}$$

Multiply \frac{13}{4} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{13\times 1}{4\times 3}}{\frac{\frac{2}{14}-\frac{5}{7}}{1+\frac{5}{6}}}$$

Do the multiplications in the fraction \frac{13\times 1}{4\times 3}.

$$\frac{\frac{13}{12}}{\frac{\frac{2}{14}-\frac{5}{7}}{1+\frac{5}{6}}}$$

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

$$\frac{\frac{13}{12}}{\frac{\frac{1}{7}-\frac{5}{7}}{1+\frac{5}{6}}}$$

Since \frac{1}{7} and \frac{5}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{13}{12}}{\frac{\frac{1-5}{7}}{1+\frac{5}{6}}}$$

Subtract 5 from 1 to get -4.

$$\frac{\frac{13}{12}}{\frac{-\frac{4}{7}}{1+\frac{5}{6}}}$$

Convert 1 to fraction \frac{6}{6}.

$$\frac{\frac{13}{12}}{\frac{-\frac{4}{7}}{\frac{6}{6}+\frac{5}{6}}}$$

Since \frac{6}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{13}{12}}{\frac{-\frac{4}{7}}{\frac{6+5}{6}}}$$

Add 6 and 5 to get 11.

$$\frac{\frac{13}{12}}{\frac{-\frac{4}{7}}{\frac{11}{6}}}$$

Divide -\frac{4}{7} by \frac{11}{6} by multiplying -\frac{4}{7} by the reciprocal of \frac{11}{6}.

$$\frac{\frac{13}{12}}{-\frac{4}{7}\times \frac{6}{11}}$$

Multiply -\frac{4}{7} times \frac{6}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{13}{12}}{\frac{-4\times 6}{7\times 11}}$$

Do the multiplications in the fraction \frac{-4\times 6}{7\times 11}.

$$\frac{\frac{13}{12}}{\frac{-24}{77}}$$

Fraction \frac{-24}{77} can be rewritten as -\frac{24}{77} by extracting the negative sign.

$$\frac{\frac{13}{12}}{-\frac{24}{77}}$$

Divide \frac{13}{12} by -\frac{24}{77} by multiplying \frac{13}{12} by the reciprocal of -\frac{24}{77}.

$$\frac{13}{12}\left(-\frac{77}{24}\right)$$

Multiply \frac{13}{12} times -\frac{77}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\left(-77\right)}{12\times 24}$$

Do the multiplications in the fraction \frac{13\left(-77\right)}{12\times 24}.

$$\frac{-1001}{288}$$

Fraction \frac{-1001}{288} can be rewritten as -\frac{1001}{288} by extracting the negative sign.

$$-\frac{1001}{288}$$

Factor

$$-\frac{1001}{288} = -3\frac{137}{288} = -3.4756944444444446$$