Solve (0,2-4/3)(-5/8)-(-5/12-9div5):21/3=

$$( 0,2 - \frac { 4 } { 3 } ) ( - \frac { 5 } { 8 } ) - ( - \frac { 5 } { 12 } - 9 \div 5 ) : 2 \frac { 1 } { 3 } =$$

Evaluate

$$\frac{199}{120}\approx 1,658333333$$

Solution Steps

Convert decimal number 0,2 to fraction \frac{2}{10}. Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\left(\frac{1}{5}-\frac{4}{3}\right)\left(-\frac{5}{8}\right)-\frac{-\frac{5}{12}-\frac{9}{5}}{\frac{2\times 3+1}{3}}$$

Least common multiple of 5 and 3 is 15. Convert \frac{1}{5} and \frac{4}{3} to fractions with denominator 15.

$$\left(\frac{3}{15}-\frac{20}{15}\right)\left(-\frac{5}{8}\right)-\frac{-\frac{5}{12}-\frac{9}{5}}{\frac{2\times 3+1}{3}}$$

Since \frac{3}{15} and \frac{20}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-20}{15}\left(-\frac{5}{8}\right)-\frac{-\frac{5}{12}-\frac{9}{5}}{\frac{2\times 3+1}{3}}$$

Subtract 20 from 3 to get -17.

$$-\frac{17}{15}\left(-\frac{5}{8}\right)-\frac{-\frac{5}{12}-\frac{9}{5}}{\frac{2\times 3+1}{3}}$$

Multiply -\frac{17}{15} times -\frac{5}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-17\left(-5\right)}{15\times 8}-\frac{-\frac{5}{12}-\frac{9}{5}}{\frac{2\times 3+1}{3}}$$

Do the multiplications in the fraction \frac{-17\left(-5\right)}{15\times 8}.

$$\frac{85}{120}-\frac{-\frac{5}{12}-\frac{9}{5}}{\frac{2\times 3+1}{3}}$$

Reduce the fraction \frac{85}{120} to lowest terms by extracting and canceling out 5.

$$\frac{17}{24}-\frac{-\frac{5}{12}-\frac{9}{5}}{\frac{2\times 3+1}{3}}$$

Least common multiple of 12 and 5 is 60. Convert -\frac{5}{12} and \frac{9}{5} to fractions with denominator 60.

$$\frac{17}{24}-\frac{-\frac{25}{60}-\frac{108}{60}}{\frac{2\times 3+1}{3}}$$

Since -\frac{25}{60} and \frac{108}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17}{24}-\frac{\frac{-25-108}{60}}{\frac{2\times 3+1}{3}}$$

Subtract 108 from -25 to get -133.

$$\frac{17}{24}-\frac{-\frac{133}{60}}{\frac{2\times 3+1}{3}}$$

Multiply 2 and 3 to get 6.

$$\frac{17}{24}-\frac{-\frac{133}{60}}{\frac{6+1}{3}}$$

Add 6 and 1 to get 7.

$$\frac{17}{24}-\frac{-\frac{133}{60}}{\frac{7}{3}}$$

Divide -\frac{133}{60} by \frac{7}{3} by multiplying -\frac{133}{60} by the reciprocal of \frac{7}{3}.

$$\frac{17}{24}-\left(-\frac{133}{60}\times \frac{3}{7}\right)$$

Multiply -\frac{133}{60} times \frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{17}{24}-\frac{-133\times 3}{60\times 7}$$

Do the multiplications in the fraction \frac{-133\times 3}{60\times 7}.

$$\frac{17}{24}-\frac{-399}{420}$$

Reduce the fraction \frac{-399}{420} to lowest terms by extracting and canceling out 21.

$$\frac{17}{24}-\left(-\frac{19}{20}\right)$$

The opposite of -\frac{19}{20} is \frac{19}{20}.

$$\frac{17}{24}+\frac{19}{20}$$

Least common multiple of 24 and 20 is 120. Convert \frac{17}{24} and \frac{19}{20} to fractions with denominator 120.

$$\frac{85}{120}+\frac{114}{120}$$

Since \frac{85}{120} and \frac{114}{120} have the same denominator, add them by adding their numerators.

$$\frac{85+114}{120}$$

Add 85 and 114 to get 199.

$$\frac{199}{120}$$

Factor

$$\frac{199}{3 \cdot 5 \cdot 2 ^ {3}} = 1\frac{79}{120} = 1.6583333333333334$$