Solve (2/5-1/2)+3/5*[7/12-frac{3}{5}:(frac{1}{4}-frac{1}{5})]

$$( \frac { 2 } { 5 } - \frac { 1 } { 2 } ) + \frac { 3 } { 5 } \cdot [ \frac { 7 } { 12 } - \frac { 3 } { 5 } : ( \frac { 1 } { 4 } - \frac { 1 } { 5 } ) ]$$

Evaluate

$$-\frac{139}{20}=-6.95$$

Solution Steps

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

$$\frac{4}{10}-\frac{5}{10}+\frac{3}{5}\left(\frac{7}{12}-\frac{\frac{3}{5}}{\frac{1}{4}-\frac{1}{5}}\right)$$

Since \frac{4}{10} and \frac{5}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-5}{10}+\frac{3}{5}\left(\frac{7}{12}-\frac{\frac{3}{5}}{\frac{1}{4}-\frac{1}{5}}\right)$$

Subtract 5 from 4 to get -1.

$$-\frac{1}{10}+\frac{3}{5}\left(\frac{7}{12}-\frac{\frac{3}{5}}{\frac{1}{4}-\frac{1}{5}}\right)$$

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{1}{5} to fractions with denominator 20.

$$-\frac{1}{10}+\frac{3}{5}\left(\frac{7}{12}-\frac{\frac{3}{5}}{\frac{5}{20}-\frac{4}{20}}\right)$$

Since \frac{5}{20} and \frac{4}{20} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{10}+\frac{3}{5}\left(\frac{7}{12}-\frac{\frac{3}{5}}{\frac{5-4}{20}}\right)$$

Subtract 4 from 5 to get 1.

$$-\frac{1}{10}+\frac{3}{5}\left(\frac{7}{12}-\frac{\frac{3}{5}}{\frac{1}{20}}\right)$$

Divide \frac{3}{5} by \frac{1}{20} by multiplying \frac{3}{5} by the reciprocal of \frac{1}{20}.

$$-\frac{1}{10}+\frac{3}{5}\left(\frac{7}{12}-\frac{3}{5}\times 20\right)$$

Express \frac{3}{5}\times 20 as a single fraction.

$$-\frac{1}{10}+\frac{3}{5}\left(\frac{7}{12}-\frac{3\times 20}{5}\right)$$

Multiply 3 and 20 to get 60.

$$-\frac{1}{10}+\frac{3}{5}\left(\frac{7}{12}-\frac{60}{5}\right)$$

Divide 60 by 5 to get 12.

$$-\frac{1}{10}+\frac{3}{5}\left(\frac{7}{12}-12\right)$$

Convert 12 to fraction \frac{144}{12}.

$$-\frac{1}{10}+\frac{3}{5}\left(\frac{7}{12}-\frac{144}{12}\right)$$

Since \frac{7}{12} and \frac{144}{12} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{10}+\frac{3}{5}\times \frac{7-144}{12}$$

Subtract 144 from 7 to get -137.

$$-\frac{1}{10}+\frac{3}{5}\left(-\frac{137}{12}\right)$$

Multiply \frac{3}{5} times -\frac{137}{12} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{1}{10}+\frac{3\left(-137\right)}{5\times 12}$$

Do the multiplications in the fraction \frac{3\left(-137\right)}{5\times 12}.

$$-\frac{1}{10}+\frac{-411}{60}$$

Reduce the fraction \frac{-411}{60} to lowest terms by extracting and canceling out 3.

$$-\frac{1}{10}-\frac{137}{20}$$

Least common multiple of 10 and 20 is 20. Convert -\frac{1}{10} and \frac{137}{20} to fractions with denominator 20.

$$-\frac{2}{20}-\frac{137}{20}$$

Since -\frac{2}{20} and \frac{137}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2-137}{20}$$

Subtract 137 from -2 to get -139.

$$-\frac{139}{20}$$

Factor

$$-\frac{139}{20} = -6\frac{19}{20} = -6.95$$