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

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

Evaluate

$$\frac{951}{2860}\approx 0.332517483$$

Solution Steps

Least common multiple of 4 and 5 is 20. Convert \frac{7}{4} and \frac{7}{5} to fractions with denominator 20.

$$\frac{\frac{35}{20}+\frac{28}{20}}{2-\frac{7}{4}\times \frac{7}{2}}+\frac{3+2\times \frac{7}{8}}{5-\frac{2}{3}}$$

Since \frac{35}{20} and \frac{28}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{35+28}{20}}{2-\frac{7}{4}\times \frac{7}{2}}+\frac{3+2\times \frac{7}{8}}{5-\frac{2}{3}}$$

Add 35 and 28 to get 63.

$$\frac{\frac{63}{20}}{2-\frac{7}{4}\times \frac{7}{2}}+\frac{3+2\times \frac{7}{8}}{5-\frac{2}{3}}$$

Multiply \frac{7}{4} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{63}{20}}{2-\frac{7\times 7}{4\times 2}}+\frac{3+2\times \frac{7}{8}}{5-\frac{2}{3}}$$

Do the multiplications in the fraction \frac{7\times 7}{4\times 2}.

$$\frac{\frac{63}{20}}{2-\frac{49}{8}}+\frac{3+2\times \frac{7}{8}}{5-\frac{2}{3}}$$

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

$$\frac{\frac{63}{20}}{\frac{16}{8}-\frac{49}{8}}+\frac{3+2\times \frac{7}{8}}{5-\frac{2}{3}}$$

Since \frac{16}{8} and \frac{49}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{63}{20}}{\frac{16-49}{8}}+\frac{3+2\times \frac{7}{8}}{5-\frac{2}{3}}$$

Subtract 49 from 16 to get -33.

$$\frac{\frac{63}{20}}{-\frac{33}{8}}+\frac{3+2\times \frac{7}{8}}{5-\frac{2}{3}}$$

Divide \frac{63}{20} by -\frac{33}{8} by multiplying \frac{63}{20} by the reciprocal of -\frac{33}{8}.

$$\frac{63}{20}\left(-\frac{8}{33}\right)+\frac{3+2\times \frac{7}{8}}{5-\frac{2}{3}}$$

Multiply \frac{63}{20} times -\frac{8}{33} by multiplying numerator times numerator and denominator times denominator.

$$\frac{63\left(-8\right)}{20\times 33}+\frac{3+2\times \frac{7}{8}}{5-\frac{2}{3}}$$

Do the multiplications in the fraction \frac{63\left(-8\right)}{20\times 33}.

$$\frac{-504}{660}+\frac{3+2\times \frac{7}{8}}{5-\frac{2}{3}}$$

Reduce the fraction \frac{-504}{660} to lowest terms by extracting and canceling out 12.

$$-\frac{42}{55}+\frac{3+2\times \frac{7}{8}}{5-\frac{2}{3}}$$

Express 2\times \frac{7}{8} as a single fraction.

$$-\frac{42}{55}+\frac{3+\frac{2\times 7}{8}}{5-\frac{2}{3}}$$

Multiply 2 and 7 to get 14.

$$-\frac{42}{55}+\frac{3+\frac{14}{8}}{5-\frac{2}{3}}$$

Reduce the fraction \frac{14}{8} to lowest terms by extracting and canceling out 2.

$$-\frac{42}{55}+\frac{3+\frac{7}{4}}{5-\frac{2}{3}}$$

Convert 3 to fraction \frac{12}{4}.

$$-\frac{42}{55}+\frac{\frac{12}{4}+\frac{7}{4}}{5-\frac{2}{3}}$$

Since \frac{12}{4} and \frac{7}{4} have the same denominator, add them by adding their numerators.

$$-\frac{42}{55}+\frac{\frac{12+7}{4}}{5-\frac{2}{3}}$$

Add 12 and 7 to get 19.

$$-\frac{42}{55}+\frac{\frac{19}{4}}{5-\frac{2}{3}}$$

Convert 5 to fraction \frac{15}{3}.

$$-\frac{42}{55}+\frac{\frac{19}{4}}{\frac{15}{3}-\frac{2}{3}}$$

Since \frac{15}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{42}{55}+\frac{\frac{19}{4}}{\frac{15-2}{3}}$$

Subtract 2 from 15 to get 13.

$$-\frac{42}{55}+\frac{\frac{19}{4}}{\frac{13}{3}}$$

Divide \frac{19}{4} by \frac{13}{3} by multiplying \frac{19}{4} by the reciprocal of \frac{13}{3}.

$$-\frac{42}{55}+\frac{19}{4}\times \frac{3}{13}$$

Multiply \frac{19}{4} times \frac{3}{13} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{42}{55}+\frac{19\times 3}{4\times 13}$$

Do the multiplications in the fraction \frac{19\times 3}{4\times 13}.

$$-\frac{42}{55}+\frac{57}{52}$$

Least common multiple of 55 and 52 is 2860. Convert -\frac{42}{55} and \frac{57}{52} to fractions with denominator 2860.

$$-\frac{2184}{2860}+\frac{3135}{2860}$$

Since -\frac{2184}{2860} and \frac{3135}{2860} have the same denominator, add them by adding their numerators.

$$\frac{-2184+3135}{2860}$$

Add -2184 and 3135 to get 951.

$$\frac{951}{2860}$$

Factor

$$\frac{3 \cdot 317}{2 ^ {2} \cdot 5 \cdot 11 \cdot 13} = 0.33251748251748253$$