Solve (7/5+3/10-4/15:5/6):(frac{1}{2}+frac{1}{5}-frac{1}{8})

$$( \frac { 7 } { 5 } + \frac { 3 } { 10 } - \frac { 4 } { 15 } : \frac { 5 } { 6 } ) : ( \frac { 1 } { 2 } + \frac { 1 } { 5 } - \frac { 1 } { 8 } )$$

Evaluate

$$\frac{12}{5}=2.4$$

Solution Steps

Least common multiple of 5 and 10 is 10. Convert \frac{7}{5} and \frac{3}{10} to fractions with denominator 10.

$$\frac{\frac{14}{10}+\frac{3}{10}-\frac{\frac{4}{15}}{\frac{5}{6}}}{\frac{1}{2}+\frac{1}{5}-\frac{1}{8}}$$

Since \frac{14}{10} and \frac{3}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{14+3}{10}-\frac{\frac{4}{15}}{\frac{5}{6}}}{\frac{1}{2}+\frac{1}{5}-\frac{1}{8}}$$

Add 14 and 3 to get 17.

$$\frac{\frac{17}{10}-\frac{\frac{4}{15}}{\frac{5}{6}}}{\frac{1}{2}+\frac{1}{5}-\frac{1}{8}}$$

Divide \frac{4}{15} by \frac{5}{6} by multiplying \frac{4}{15} by the reciprocal of \frac{5}{6}.

$$\frac{\frac{17}{10}-\frac{4}{15}\times \frac{6}{5}}{\frac{1}{2}+\frac{1}{5}-\frac{1}{8}}$$

Multiply \frac{4}{15} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{17}{10}-\frac{4\times 6}{15\times 5}}{\frac{1}{2}+\frac{1}{5}-\frac{1}{8}}$$

Do the multiplications in the fraction \frac{4\times 6}{15\times 5}.

$$\frac{\frac{17}{10}-\frac{24}{75}}{\frac{1}{2}+\frac{1}{5}-\frac{1}{8}}$$

Reduce the fraction \frac{24}{75} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{17}{10}-\frac{8}{25}}{\frac{1}{2}+\frac{1}{5}-\frac{1}{8}}$$

Least common multiple of 10 and 25 is 50. Convert \frac{17}{10} and \frac{8}{25} to fractions with denominator 50.

$$\frac{\frac{85}{50}-\frac{16}{50}}{\frac{1}{2}+\frac{1}{5}-\frac{1}{8}}$$

Since \frac{85}{50} and \frac{16}{50} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{85-16}{50}}{\frac{1}{2}+\frac{1}{5}-\frac{1}{8}}$$

Subtract 16 from 85 to get 69.

$$\frac{\frac{69}{50}}{\frac{1}{2}+\frac{1}{5}-\frac{1}{8}}$$

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{1}{5} to fractions with denominator 10.

$$\frac{\frac{69}{50}}{\frac{5}{10}+\frac{2}{10}-\frac{1}{8}}$$

Since \frac{5}{10} and \frac{2}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{69}{50}}{\frac{5+2}{10}-\frac{1}{8}}$$

Add 5 and 2 to get 7.

$$\frac{\frac{69}{50}}{\frac{7}{10}-\frac{1}{8}}$$

Least common multiple of 10 and 8 is 40. Convert \frac{7}{10} and \frac{1}{8} to fractions with denominator 40.

$$\frac{\frac{69}{50}}{\frac{28}{40}-\frac{5}{40}}$$

Since \frac{28}{40} and \frac{5}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{69}{50}}{\frac{28-5}{40}}$$

Subtract 5 from 28 to get 23.

$$\frac{\frac{69}{50}}{\frac{23}{40}}$$

Divide \frac{69}{50} by \frac{23}{40} by multiplying \frac{69}{50} by the reciprocal of \frac{23}{40}.

$$\frac{69}{50}\times \frac{40}{23}$$

Multiply \frac{69}{50} times \frac{40}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{69\times 40}{50\times 23}$$

Do the multiplications in the fraction \frac{69\times 40}{50\times 23}.

$$\frac{2760}{1150}$$

Reduce the fraction \frac{2760}{1150} to lowest terms by extracting and canceling out 230.

$$\frac{12}{5}$$

Factor

$$\frac{2 ^ {2} \cdot 3}{5} = 2\frac{2}{5} = 2.4$$