Solve 3/8+5/3-8/5/frac{2{5}+frac{3}{5}divfrac{7}{4}}

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

Evaluate

$$\frac{371}{624}\approx 0.594551282$$

Solution Steps

Least common multiple of 8 and 3 is 24. Convert \frac{3}{8} and \frac{5}{3} to fractions with denominator 24.

$$\frac{\frac{9}{24}+\frac{40}{24}-\frac{8}{5}}{\frac{2}{5}+\frac{\frac{3}{5}}{\frac{7}{4}}}$$

Since \frac{9}{24} and \frac{40}{24} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9+40}{24}-\frac{8}{5}}{\frac{2}{5}+\frac{\frac{3}{5}}{\frac{7}{4}}}$$

Add 9 and 40 to get 49.

$$\frac{\frac{49}{24}-\frac{8}{5}}{\frac{2}{5}+\frac{\frac{3}{5}}{\frac{7}{4}}}$$

Least common multiple of 24 and 5 is 120. Convert \frac{49}{24} and \frac{8}{5} to fractions with denominator 120.

$$\frac{\frac{245}{120}-\frac{192}{120}}{\frac{2}{5}+\frac{\frac{3}{5}}{\frac{7}{4}}}$$

Since \frac{245}{120} and \frac{192}{120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{245-192}{120}}{\frac{2}{5}+\frac{\frac{3}{5}}{\frac{7}{4}}}$$

Subtract 192 from 245 to get 53.

$$\frac{\frac{53}{120}}{\frac{2}{5}+\frac{\frac{3}{5}}{\frac{7}{4}}}$$

Divide \frac{3}{5} by \frac{7}{4} by multiplying \frac{3}{5} by the reciprocal of \frac{7}{4}.

$$\frac{\frac{53}{120}}{\frac{2}{5}+\frac{3}{5}\times \frac{4}{7}}$$

Multiply \frac{3}{5} times \frac{4}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{53}{120}}{\frac{2}{5}+\frac{3\times 4}{5\times 7}}$$

Do the multiplications in the fraction \frac{3\times 4}{5\times 7}.

$$\frac{\frac{53}{120}}{\frac{2}{5}+\frac{12}{35}}$$

Least common multiple of 5 and 35 is 35. Convert \frac{2}{5} and \frac{12}{35} to fractions with denominator 35.

$$\frac{\frac{53}{120}}{\frac{14}{35}+\frac{12}{35}}$$

Since \frac{14}{35} and \frac{12}{35} have the same denominator, add them by adding their numerators.

$$\frac{\frac{53}{120}}{\frac{14+12}{35}}$$

Add 14 and 12 to get 26.

$$\frac{\frac{53}{120}}{\frac{26}{35}}$$

Divide \frac{53}{120} by \frac{26}{35} by multiplying \frac{53}{120} by the reciprocal of \frac{26}{35}.

$$\frac{53}{120}\times \frac{35}{26}$$

Multiply \frac{53}{120} times \frac{35}{26} by multiplying numerator times numerator and denominator times denominator.

$$\frac{53\times 35}{120\times 26}$$

Do the multiplications in the fraction \frac{53\times 35}{120\times 26}.

$$\frac{1855}{3120}$$

Reduce the fraction \frac{1855}{3120} to lowest terms by extracting and canceling out 5.

$$\frac{371}{624}$$

Factor

$$\frac{7 \cdot 53}{2 ^ {4} \cdot 3 \cdot 13} = 0.594551282051282$$