Solve 2/5-(1/12-4/9div8/15)div(-2frac{1}{10})

$$\frac { 2 } { 5 } - ( \frac { 1 } { 12 } - \frac { 4 } { 9 } \div \frac { 8 } { 15 } ) \div ( - 2 \frac { 1 } { 10 } )$$

Evaluate

$$\frac{3}{70}\approx 0.042857143$$

Solution Steps

Divide \frac{4}{9} by \frac{8}{15} by multiplying \frac{4}{9} by the reciprocal of \frac{8}{15}.

$$\frac{2}{5}-\frac{\frac{1}{12}-\frac{4}{9}\times \frac{15}{8}}{-\frac{2\times 10+1}{10}}$$

Multiply \frac{4}{9} times \frac{15}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{5}-\frac{\frac{1}{12}-\frac{4\times 15}{9\times 8}}{-\frac{2\times 10+1}{10}}$$

Do the multiplications in the fraction \frac{4\times 15}{9\times 8}.

$$\frac{2}{5}-\frac{\frac{1}{12}-\frac{60}{72}}{-\frac{2\times 10+1}{10}}$$

Reduce the fraction \frac{60}{72} to lowest terms by extracting and canceling out 12.

$$\frac{2}{5}-\frac{\frac{1}{12}-\frac{5}{6}}{-\frac{2\times 10+1}{10}}$$

Least common multiple of 12 and 6 is 12. Convert \frac{1}{12} and \frac{5}{6} to fractions with denominator 12.

$$\frac{2}{5}-\frac{\frac{1}{12}-\frac{10}{12}}{-\frac{2\times 10+1}{10}}$$

Since \frac{1}{12} and \frac{10}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{5}-\frac{\frac{1-10}{12}}{-\frac{2\times 10+1}{10}}$$

Subtract 10 from 1 to get -9.

$$\frac{2}{5}-\frac{\frac{-9}{12}}{-\frac{2\times 10+1}{10}}$$

Reduce the fraction \frac{-9}{12} to lowest terms by extracting and canceling out 3.

$$\frac{2}{5}-\frac{-\frac{3}{4}}{-\frac{2\times 10+1}{10}}$$

Multiply 2 and 10 to get 20.

$$\frac{2}{5}-\frac{-\frac{3}{4}}{-\frac{20+1}{10}}$$

Add 20 and 1 to get 21.

$$\frac{2}{5}-\frac{-\frac{3}{4}}{-\frac{21}{10}}$$

Divide -\frac{3}{4} by -\frac{21}{10} by multiplying -\frac{3}{4} by the reciprocal of -\frac{21}{10}.

$$\frac{2}{5}-\left(-\frac{3}{4}\left(-\frac{10}{21}\right)\right)$$

Multiply -\frac{3}{4} times -\frac{10}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{5}-\frac{-3\left(-10\right)}{4\times 21}$$

Do the multiplications in the fraction \frac{-3\left(-10\right)}{4\times 21}.

$$\frac{2}{5}-\frac{30}{84}$$

Reduce the fraction \frac{30}{84} to lowest terms by extracting and canceling out 6.

$$\frac{2}{5}-\frac{5}{14}$$

Least common multiple of 5 and 14 is 70. Convert \frac{2}{5} and \frac{5}{14} to fractions with denominator 70.

$$\frac{28}{70}-\frac{25}{70}$$

Since \frac{28}{70} and \frac{25}{70} have the same denominator, subtract them by subtracting their numerators.

$$\frac{28-25}{70}$$

Subtract 25 from 28 to get 3.

$$\frac{3}{70}$$

Factor

$$\frac{3}{2 \cdot 5 \cdot 7} = 0.04285714285714286$$