Solve (1/5+1/4)-(-1/30)/(-1frac{2{5})*(-1frac{1}{4})}

$$\frac { ( \frac { 1 } { 5 } + \frac { 1 } { 4 } ) - ( - \frac { 1 } { 30 } ) } { ( - 1 \frac { 2 } { 5 } ) \times ( - 1 \frac { 1 } { 4 } ) }$$

Evaluate

$$\frac{29}{105}\approx 0.276190476$$

Solution Steps

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

$$\frac{\frac{4}{20}+\frac{5}{20}-\left(-\frac{1}{30}\right)}{\left(-\frac{1\times 5+2}{5}\right)\left(-\frac{1\times 4+1}{4}\right)}$$

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

$$\frac{\frac{4+5}{20}-\left(-\frac{1}{30}\right)}{\left(-\frac{1\times 5+2}{5}\right)\left(-\frac{1\times 4+1}{4}\right)}$$

Add 4 and 5 to get 9.

$$\frac{\frac{9}{20}-\left(-\frac{1}{30}\right)}{\left(-\frac{1\times 5+2}{5}\right)\left(-\frac{1\times 4+1}{4}\right)}$$

The opposite of -\frac{1}{30} is \frac{1}{30}.

$$\frac{\frac{9}{20}+\frac{1}{30}}{\left(-\frac{1\times 5+2}{5}\right)\left(-\frac{1\times 4+1}{4}\right)}$$

Least common multiple of 20 and 30 is 60. Convert \frac{9}{20} and \frac{1}{30} to fractions with denominator 60.

$$\frac{\frac{27}{60}+\frac{2}{60}}{\left(-\frac{1\times 5+2}{5}\right)\left(-\frac{1\times 4+1}{4}\right)}$$

Since \frac{27}{60} and \frac{2}{60} have the same denominator, add them by adding their numerators.

$$\frac{\frac{27+2}{60}}{\left(-\frac{1\times 5+2}{5}\right)\left(-\frac{1\times 4+1}{4}\right)}$$

Add 27 and 2 to get 29.

$$\frac{\frac{29}{60}}{\left(-\frac{1\times 5+2}{5}\right)\left(-\frac{1\times 4+1}{4}\right)}$$

Multiply 1 and 5 to get 5.

$$\frac{\frac{29}{60}}{\left(-\frac{5+2}{5}\right)\left(-\frac{1\times 4+1}{4}\right)}$$

Add 5 and 2 to get 7.

$$\frac{\frac{29}{60}}{-\frac{7}{5}\left(-\frac{4+1}{4}\right)}$$

Add 4 and 1 to get 5.

$$\frac{\frac{29}{60}}{-\frac{7}{5}\left(-\frac{5}{4}\right)}$$

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

$$\frac{\frac{29}{60}}{\frac{-7\left(-5\right)}{5\times 4}}$$

Do the multiplications in the fraction \frac{-7\left(-5\right)}{5\times 4}.

$$\frac{\frac{29}{60}}{\frac{35}{20}}$$

Reduce the fraction \frac{35}{20} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{29}{60}}{\frac{7}{4}}$$

Divide \frac{29}{60} by \frac{7}{4} by multiplying \frac{29}{60} by the reciprocal of \frac{7}{4}.

$$\frac{29}{60}\times \frac{4}{7}$$

Multiply \frac{29}{60} times \frac{4}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{29\times 4}{60\times 7}$$

Do the multiplications in the fraction \frac{29\times 4}{60\times 7}.

$$\frac{116}{420}$$

Reduce the fraction \frac{116}{420} to lowest terms by extracting and canceling out 4.

$$\frac{29}{105}$$

Factor

$$\frac{29}{3 \cdot 5 \cdot 7} = 0.2761904761904762$$