Solve 5/7+8/5/3div1-frac{1/5}{frac{5}{6}+1}

$$\frac { \frac { 5 } { 7 } + \frac { 8 } { 5 } } { 3 } \div \frac { 1 - \frac { 1 } { 5 } } { \frac { 5 } { 6 } + 1 }$$

Evaluate

$$\frac{99}{56}\approx 1.767857143$$

Solution Steps

Divide \frac{\frac{5}{7}+\frac{8}{5}}{3} by \frac{1-\frac{1}{5}}{\frac{5}{6}+1} by multiplying \frac{\frac{5}{7}+\frac{8}{5}}{3} by the reciprocal of \frac{1-\frac{1}{5}}{\frac{5}{6}+1}.

$$\frac{\left(\frac{5}{7}+\frac{8}{5}\right)\left(\frac{5}{6}+1\right)}{3\left(1-\frac{1}{5}\right)}$$

Least common multiple of 7 and 5 is 35. Convert \frac{5}{7} and \frac{8}{5} to fractions with denominator 35.

$$\frac{\left(\frac{25}{35}+\frac{56}{35}\right)\left(\frac{5}{6}+1\right)}{3\left(1-\frac{1}{5}\right)}$$

Since \frac{25}{35} and \frac{56}{35} have the same denominator, add them by adding their numerators.

$$\frac{\frac{25+56}{35}\left(\frac{5}{6}+1\right)}{3\left(1-\frac{1}{5}\right)}$$

Add 25 and 56 to get 81.

$$\frac{\frac{81}{35}\left(\frac{5}{6}+1\right)}{3\left(1-\frac{1}{5}\right)}$$

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

$$\frac{\frac{81}{35}\left(\frac{5}{6}+\frac{6}{6}\right)}{3\left(1-\frac{1}{5}\right)}$$

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

$$\frac{\frac{81}{35}\times \frac{5+6}{6}}{3\left(1-\frac{1}{5}\right)}$$

Add 5 and 6 to get 11.

$$\frac{\frac{81}{35}\times \frac{11}{6}}{3\left(1-\frac{1}{5}\right)}$$

Multiply \frac{81}{35} times \frac{11}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{81\times 11}{35\times 6}}{3\left(1-\frac{1}{5}\right)}$$

Do the multiplications in the fraction \frac{81\times 11}{35\times 6}.

$$\frac{\frac{891}{210}}{3\left(1-\frac{1}{5}\right)}$$

Reduce the fraction \frac{891}{210} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{297}{70}}{3\left(1-\frac{1}{5}\right)}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{\frac{297}{70}}{3\left(\frac{5}{5}-\frac{1}{5}\right)}$$

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

$$\frac{\frac{297}{70}}{3\times \frac{5-1}{5}}$$

Subtract 1 from 5 to get 4.

$$\frac{\frac{297}{70}}{3\times \frac{4}{5}}$$

Express 3\times \frac{4}{5} as a single fraction.

$$\frac{\frac{297}{70}}{\frac{3\times 4}{5}}$$

Multiply 3 and 4 to get 12.

$$\frac{\frac{297}{70}}{\frac{12}{5}}$$

Divide \frac{297}{70} by \frac{12}{5} by multiplying \frac{297}{70} by the reciprocal of \frac{12}{5}.

$$\frac{297}{70}\times \frac{5}{12}$$

Multiply \frac{297}{70} times \frac{5}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{297\times 5}{70\times 12}$$

Do the multiplications in the fraction \frac{297\times 5}{70\times 12}.

$$\frac{1485}{840}$$

Reduce the fraction \frac{1485}{840} to lowest terms by extracting and canceling out 15.

$$\frac{99}{56}$$

Factor

$$\frac{3 ^ {2} \cdot 11}{2 ^ {3} \cdot 7} = 1\frac{43}{56} = 1.7678571428571428$$