Solve (2-7/8)*8/9:(5/8+5/6)=

$$( 2 - \frac { 7 } { 8 } ) \cdot \frac { 8 } { 9 } : ( \frac { 5 } { 8 } + \frac { 5 } { 6 } ) =$$

Evaluate

$$\frac{24}{35}\approx 0.685714286$$

Solution Steps

Convert 2 to fraction \frac{16}{8}.

$$\frac{\left(\frac{16}{8}-\frac{7}{8}\right)\times \frac{8}{9}}{\frac{5}{8}+\frac{5}{6}}$$

Since \frac{16}{8} and \frac{7}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{16-7}{8}\times \frac{8}{9}}{\frac{5}{8}+\frac{5}{6}}$$

Subtract 7 from 16 to get 9.

$$\frac{\frac{9}{8}\times \frac{8}{9}}{\frac{5}{8}+\frac{5}{6}}$$

Cancel out \frac{9}{8} and its reciprocal \frac{8}{9}.

$$\frac{1}{\frac{5}{8}+\frac{5}{6}}$$

Least common multiple of 8 and 6 is 24. Convert \frac{5}{8} and \frac{5}{6} to fractions with denominator 24.

$$\frac{1}{\frac{15}{24}+\frac{20}{24}}$$

Since \frac{15}{24} and \frac{20}{24} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{15+20}{24}}$$

Add 15 and 20 to get 35.

$$\frac{1}{\frac{35}{24}}$$

Divide 1 by \frac{35}{24} by multiplying 1 by the reciprocal of \frac{35}{24}.

$$1\times \frac{24}{35}$$

Multiply 1 and \frac{24}{35} to get \frac{24}{35}.

$$\frac{24}{35}$$

Factor

$$\frac{2 ^ {3} \cdot 3}{5 \cdot 7} = 0.6857142857142857$$