Solve 5/7+8/5/3/frac{1-frac{1{4}}{frac{5}{6}+1}}

$$\frac{ \frac{ \frac{ 5 }{ 7 } + \frac{ 8 }{ 5 } }{ 3 } }{ \frac{ 1- \frac{ 1 }{ 4 } }{ \frac{ 5 }{ 6 } +1 } }$$

Evaluate

$$\frac{66}{35}\approx 1.885714286$$

Solution Steps

Divide \frac{\frac{5}{7}+\frac{8}{5}}{3} by \frac{1-\frac{1}{4}}{\frac{5}{6}+1} by multiplying \frac{\frac{5}{7}+\frac{8}{5}}{3} by the reciprocal of \frac{1-\frac{1}{4}}{\frac{5}{6}+1}.

$$\frac{\left(\frac{5}{7}+\frac{8}{5}\right)\left(\frac{5}{6}+1\right)}{3\left(1-\frac{1}{4}\right)}$$

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

$$\frac{\left(\frac{25}{35}+\frac{56}{35}\right)\left(\frac{5}{6}+1\right)}{3\left(1-\frac{1}{4}\right)}$$

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

$$\frac{\frac{25+56}{35}\left(\frac{5}{6}+1\right)}{3\left(1-\frac{1}{4}\right)}$$

Add 25 and 56 to get 81.

$$\frac{\frac{81}{35}\left(\frac{5}{6}+1\right)}{3\left(1-\frac{1}{4}\right)}$$

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

$$\frac{\frac{81}{35}\left(\frac{5}{6}+\frac{6}{6}\right)}{3\left(1-\frac{1}{4}\right)}$$

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

$$\frac{\frac{81}{35}\times \frac{5+6}{6}}{3\left(1-\frac{1}{4}\right)}$$

Add 5 and 6 to get 11.

$$\frac{\frac{81}{35}\times \frac{11}{6}}{3\left(1-\frac{1}{4}\right)}$$

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

$$\frac{\frac{81\times 11}{35\times 6}}{3\left(1-\frac{1}{4}\right)}$$

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

$$\frac{\frac{891}{210}}{3\left(1-\frac{1}{4}\right)}$$

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

$$\frac{\frac{297}{70}}{3\left(1-\frac{1}{4}\right)}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{\frac{297}{70}}{3\left(\frac{4}{4}-\frac{1}{4}\right)}$$

Since \frac{4}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{297}{70}}{3\times \frac{4-1}{4}}$$

Subtract 1 from 4 to get 3.

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

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

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

Multiply 3 and 3 to get 9.

$$\frac{\frac{297}{70}}{\frac{9}{4}}$$

Divide \frac{297}{70} by \frac{9}{4} by multiplying \frac{297}{70} by the reciprocal of \frac{9}{4}.

$$\frac{297}{70}\times \frac{4}{9}$$

Multiply \frac{297}{70} times \frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{297\times 4}{70\times 9}$$

Do the multiplications in the fraction \frac{297\times 4}{70\times 9}.

$$\frac{1188}{630}$$

Reduce the fraction \frac{1188}{630} to lowest terms by extracting and canceling out 18.

$$\frac{66}{35}$$

Factor

$$\frac{2 \cdot 3 \cdot 11}{5 \cdot 7} = 1\frac{31}{35} = 1.8857142857142857$$