Solve (2-3/4-5/8)+-3+5/2/2frac{7{3}-frac{5}{6}}

$$( 2 - \frac { 3 } { 4 } - \frac { 5 } { 8 } ) + \frac { - 3 + \frac { 5 } { 2 } } { 2 \frac { 7 } { 3 } - \frac { 5 } { 6 } }$$

Evaluate

$$\frac{27}{56}\approx 0.482142857$$

Solution Steps

Convert 2 to fraction \frac{8}{4}.

$$\frac{8}{4}-\frac{3}{4}-\frac{5}{8}+\frac{-3+\frac{5}{2}}{\frac{2\times 3+7}{3}-\frac{5}{6}}$$

Since \frac{8}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-3}{4}-\frac{5}{8}+\frac{-3+\frac{5}{2}}{\frac{2\times 3+7}{3}-\frac{5}{6}}$$

Subtract 3 from 8 to get 5.

$$\frac{5}{4}-\frac{5}{8}+\frac{-3+\frac{5}{2}}{\frac{2\times 3+7}{3}-\frac{5}{6}}$$

Least common multiple of 4 and 8 is 8. Convert \frac{5}{4} and \frac{5}{8} to fractions with denominator 8.

$$\frac{10}{8}-\frac{5}{8}+\frac{-3+\frac{5}{2}}{\frac{2\times 3+7}{3}-\frac{5}{6}}$$

Since \frac{10}{8} and \frac{5}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-5}{8}+\frac{-3+\frac{5}{2}}{\frac{2\times 3+7}{3}-\frac{5}{6}}$$

Subtract 5 from 10 to get 5.

$$\frac{5}{8}+\frac{-3+\frac{5}{2}}{\frac{2\times 3+7}{3}-\frac{5}{6}}$$

Convert -3 to fraction -\frac{6}{2}.

$$\frac{5}{8}+\frac{-\frac{6}{2}+\frac{5}{2}}{\frac{2\times 3+7}{3}-\frac{5}{6}}$$

Since -\frac{6}{2} and \frac{5}{2} have the same denominator, add them by adding their numerators.

$$\frac{5}{8}+\frac{\frac{-6+5}{2}}{\frac{2\times 3+7}{3}-\frac{5}{6}}$$

Add -6 and 5 to get -1.

$$\frac{5}{8}+\frac{-\frac{1}{2}}{\frac{2\times 3+7}{3}-\frac{5}{6}}$$

Multiply 2 and 3 to get 6.

$$\frac{5}{8}+\frac{-\frac{1}{2}}{\frac{6+7}{3}-\frac{5}{6}}$$

Add 6 and 7 to get 13.

$$\frac{5}{8}+\frac{-\frac{1}{2}}{\frac{13}{3}-\frac{5}{6}}$$

Least common multiple of 3 and 6 is 6. Convert \frac{13}{3} and \frac{5}{6} to fractions with denominator 6.

$$\frac{5}{8}+\frac{-\frac{1}{2}}{\frac{26}{6}-\frac{5}{6}}$$

Since \frac{26}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{8}+\frac{-\frac{1}{2}}{\frac{26-5}{6}}$$

Subtract 5 from 26 to get 21.

$$\frac{5}{8}+\frac{-\frac{1}{2}}{\frac{21}{6}}$$

Reduce the fraction \frac{21}{6} to lowest terms by extracting and canceling out 3.

$$\frac{5}{8}+\frac{-\frac{1}{2}}{\frac{7}{2}}$$

Divide -\frac{1}{2} by \frac{7}{2} by multiplying -\frac{1}{2} by the reciprocal of \frac{7}{2}.

$$\frac{5}{8}-\frac{1}{2}\times \frac{2}{7}$$

Multiply -\frac{1}{2} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{8}+\frac{-2}{2\times 7}$$

Cancel out 2 in both numerator and denominator.

$$\frac{5}{8}+\frac{-1}{7}$$

Fraction \frac{-1}{7} can be rewritten as -\frac{1}{7} by extracting the negative sign.

$$\frac{5}{8}-\frac{1}{7}$$

Least common multiple of 8 and 7 is 56. Convert \frac{5}{8} and \frac{1}{7} to fractions with denominator 56.

$$\frac{35}{56}-\frac{8}{56}$$

Since \frac{35}{56} and \frac{8}{56} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35-8}{56}$$

Subtract 8 from 35 to get 27.

$$\frac{27}{56}$$

Factor

$$\frac{3 ^ {3}}{2 ^ {3} \cdot 7} = 0.48214285714285715$$