Solve (3/5+1/8-7/24)*3frac{1/13}{5-frac{2}{3}}

$$\frac { ( \frac { 3 } { 5 } + \frac { 1 } { 8 } - \frac { 7 } { 24 } ) \times 3 \frac { 1 } { 13 } } { 5 - \frac { 2 } { 3 } }$$

Evaluate

$$\frac{4}{13}\approx 0.307692308$$

Solution Steps

Least common multiple of 5 and 8 is 40. Convert \frac{3}{5} and \frac{1}{8} to fractions with denominator 40.

$$\frac{\left(\frac{24}{40}+\frac{5}{40}-\frac{7}{24}\right)\times \frac{3\times 13+1}{13}}{5-\frac{2}{3}}$$

Since \frac{24}{40} and \frac{5}{40} have the same denominator, add them by adding their numerators.

$$\frac{\left(\frac{24+5}{40}-\frac{7}{24}\right)\times \frac{3\times 13+1}{13}}{5-\frac{2}{3}}$$

Add 24 and 5 to get 29.

$$\frac{\left(\frac{29}{40}-\frac{7}{24}\right)\times \frac{3\times 13+1}{13}}{5-\frac{2}{3}}$$

Least common multiple of 40 and 24 is 120. Convert \frac{29}{40} and \frac{7}{24} to fractions with denominator 120.

$$\frac{\left(\frac{87}{120}-\frac{35}{120}\right)\times \frac{3\times 13+1}{13}}{5-\frac{2}{3}}$$

Since \frac{87}{120} and \frac{35}{120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{87-35}{120}\times \frac{3\times 13+1}{13}}{5-\frac{2}{3}}$$

Subtract 35 from 87 to get 52.

$$\frac{\frac{52}{120}\times \frac{3\times 13+1}{13}}{5-\frac{2}{3}}$$

Reduce the fraction \frac{52}{120} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{13}{30}\times \frac{3\times 13+1}{13}}{5-\frac{2}{3}}$$

Multiply 3 and 13 to get 39.

$$\frac{\frac{13}{30}\times \frac{39+1}{13}}{5-\frac{2}{3}}$$

Add 39 and 1 to get 40.

$$\frac{\frac{13}{30}\times \frac{40}{13}}{5-\frac{2}{3}}$$

Multiply \frac{13}{30} times \frac{40}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{13\times 40}{30\times 13}}{5-\frac{2}{3}}$$

Cancel out 13 in both numerator and denominator.

$$\frac{\frac{40}{30}}{5-\frac{2}{3}}$$

Reduce the fraction \frac{40}{30} to lowest terms by extracting and canceling out 10.

$$\frac{\frac{4}{3}}{5-\frac{2}{3}}$$

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

$$\frac{\frac{4}{3}}{\frac{15}{3}-\frac{2}{3}}$$

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

$$\frac{\frac{4}{3}}{\frac{15-2}{3}}$$

Subtract 2 from 15 to get 13.

$$\frac{\frac{4}{3}}{\frac{13}{3}}$$

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

$$\frac{4}{3}\times \frac{3}{13}$$

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

$$\frac{4\times 3}{3\times 13}$$

Cancel out 3 in both numerator and denominator.

$$\frac{4}{13}$$

Factor

$$\frac{2 ^ {2}}{13} = 0.3076923076923077$$